Peloponnese or Islands

"August" is a big stretch ... where would your 12 days come? It will of course be THE most crowded month of all... since the whole of Europe jumps into jumbo jets and dumps on all the islands for the month ... and the week of Agu 10 - Sunday Aug 18 will be the crowdiest of all, since Aug 15 is the BIGGIE Greek Holiday -- biggest of year next to Easter -- and all the Greeks take that time off to hit the beaches. After August 19th, the mob scene tapers off a bit, because Europeans have to start getting their kids back in school. How old are "young kids"? 4 & 6 are one thing... 2 and 4 are another. I think you have to be realistic, scale back on what can be done in a day.

ISLANDS -- Yes you wouldn't need a car on islands, but getting to/from can be awful hassle in August, and costly -- flights to Naxos will be $$$ On the other hand, dealing with 2 young kids on a big conventional ferry, every seat full (august), for 5.5 hours... woo. I have seen too many moms wearily walking their restless kids up and down the aisles, up and down up and down. Funny I don't see many dads doing it, maybe u are a Hero Dad. but it's draining. "fast-ferries" are 3+ hours but cost 2x as much and no decks, all reserved indoor seats, no place to walk. Mykonos in August for families is Madness. No other word for it, unless you are sinfully affluent. Example: 2 sunbeds + umbrella for day on Naxos = €7-8... on Mykonos, ONE sunbed in August can be €20. There's a daytrip from Naxos, but why? And what is this about flying back to USA from Mykonos? Not as nonstop.... you can only fly to a major European Airport & change, or fly to ATH.

PELOPONNESE -- For example, in the extreme heat of August (and even in the lesser heat of May) a day trip to Corinth-Mycenae-Epidaurus is madness. I would do Mycenae only if one could arrive 9 am to beat the crowds. With kids I'd skip Mycenae, do Tiryns &Epidaurus. Do not consider Olympia in any itinerary... way too far, on other side of Pelops, with kids in car. Look up Nemea, it's another "sacred games site" right off highway enroute to Nafplio -- great fun, easy stop: THe Revived Nemean Games will just have been over (June 24-26) - https://nemeangames.org With Kids, Delphi should be an over-nite. 3.5 hour drive each way from airport.

Nafplio is great, plenty of beaches around, no need to stay in Napflio Old Town if u have a car. With little kids, Old Town in hot weather OK to wander by day, maybe not to stay there, no lodgings have pools. Nearby Tolo Beach is a cram-jam package-holiday beach for BRIts, but just up the road, at the (never-crowded) beach at Asine, its serene -- there are several right off the sands: Porto Assini & Sofia Apts, and just 100 yards back from beach Villa Christina.

I don't know if I can advise, but I can give my perspective as a mom of 3 who traveled to the Peloponnese and Naxos, and Athens in August. My kids are older (they were 10, 13, 15 for that trip). We did go to Corinth, Mycenae, and Epidauros, and Olympia, but not Delphi.
First Peloponnese: I loved it, and found it interesting that so many people seem to go to Athens + Islands. We did have a car, and I agree that you cant do much without one - even staying in Nafplio and getting to Mycenae and Epidauros. I think bus transport is available to all of these (to Nafplio, and from Nafplio to the sites), but its so much nicer to see these on your own terms, esp. with kids. We enjoyed Nafplio and the surrounding sites a lot. We stopped at the Corinth canal en route and walked across, and that was great too. The beaches there are rocks, so bring water shoes. Without them, the foot discomfort is no joke (and I am no slouch).
Olympia was so cool. We loved that too, but yes, it is a significant drive from Nafplio. We actually spent 10 days in the Peloponnese so were able to stop and stay at other sites en route (we drove through the Arcadia mountains en route to Olympia and hiked part of the Menalon trail). I think the drive from Delphi to Olympia might be more direct, if I remember right. You could start in Nafplio lovely town + ruins), then go to Delphi (ruins), then Olympia (etc), then Stoupa/Kardamyli (beach beauty), and end in Athens. But thats a lot of moves and you said you don't want a lot. Long story short, yes the area requires a car, yes it is beautiful (!), and in our 10 days we didnt do nearly all the things we wanted )and we moved a lot). The Peloponnese could bee a very satisfying trip.
Naxos: we didnt stay in the main part of the city because by that time in our trip we wanted the tourist crush to be less immediate. We stayed south near a beach, which had a bus that connected to town in 15 minutes if desired. Loved where we were and glad we didnt stay in the town (we went there to walk around for a day which is all it took to see and do the town). We also spent a lot of time in the mountains and villages of the island, and for this we rented a car, and again, I would not want to do it on a bus for the reasons mentioned before. It was nice to have our own schedule. There were some amazing churches with frescos that I enjoyed, and we went to the village with the marble stone walkways. We spent a good deal of time on the sand beach (although we are not beach people). We enjoyed Naxos a lot, but culturally, the Peloponnese had much more to offer.
You've been to the islands; there is a sense of island vacation life, blue sky breezy, some cultural artifacts. In the Pelopnnese I felt like I was in history.
Can your kids nap in carseats? Honestly, if I were doing this trip with young kids I would throw their schedule out the window. I was kind of a nap nazi when my kids were young, and now that they're older I wonder why. Also, the hours are different in Greece - people stay up and out so late that their schedule will be thrown anyway. Add jet lag to that and who knows when they might nap. Dont hamper yourselves trying to figure that out (but maybe they aren't the kids who will sleep in a car, in which case the schedule matters more. Not presuming or judging)
On the upside, you cannot do it all by half in 12 days, and anything you choose will be magical (and equivalent in terms of car/bus decision) so beachy village island or cultural village beach? ;p

We’ve had 2 Greece trips in the past 19 months - second (last month) was just Crete, first one Eastertime last year) was mostly Peloponnese. But we got in an island, too, on that first trip, Rick Steves’ beloved Hydra. So you can have island time and the Peloponnese peninsula on the same trip!

Since Hydra is relatively close to Athens, compared to islands you mention, that makes it a great, accessible place. We ferried to Hydra then on to the Peloponnese, where we rented a car (local Pop’s Car Rental - offices in several Greek towns and cities), doing mostly 2-nighters, and two 1-night stays, moving most of the time. You may want to just stick to a section of the Peloponnese if you’re not planning on having a car, and especially if you want to stay at a place for more than a couple nights.

A surprising treat, fairly close to Napflio, was Nemea, an ancient site with a temple, other fine buildings, and an Olympia-type stadium, complete with a unique tunnel leading to the stadium. We had it all to ourselves! Their smallish museum was also well worth the time to get there, if you can find the means, and certainly if going way west to Olympia isn’t on you agenda this trip.

As we had a car, we didn’t investigate taking public transportation over land, or signing on to a day tour, or hiring a private driver/guide for a day or more, but those could all be possible options.

How young are the kids?
In August, I'd consider driving to the Peloponnese, but to some small town in the Mani or far west and just chilling. I can't see a very young child (like under 7) getting much out of the sights near Nafplio, so just easily getting somewhere with a great beach without a ferry or flight sounds nice. Look at Gialova, Pilos--but I also assume those will be mobbed in August and you'd want to book quite early. Look also at some small towns near Delphi--there was a great article in the NYT about that area earlier this year.

Thanks everyone for the comments! Very helpful. Our kids are young, 2 and 4, and certainly won't appreciate the trip. But their parents love traveling too much to just wait around for a few more years. Fortunately, my mom is there so we will have some childcare help. And yes, August will be tough, but don't have much choice on that front unfortunately. So lots of strikes against us, but we are determined to have a great trip :). Based on the comments, I'm leaning towards the Pelopennese with a car for some limited day trips - splitting time with a few days each in Nafplio or Hydra and the Mani or Pilos area. Even though the tourist crush in Greece is probably terrible everywhere you go, my sense of it based on my research is the Pelopennese is a lot less touristy than the Cyclades on a relative basis. But please correct me if I am wrong.

Hydra has no beaches to speak of. If you are going to choose a Saronic Island, look at Aegina... just 1 hour on an open-deck ferry (do NOT choose a hydrofoil)... very enjoyable seascape -- giant cruise ships, freighters, ferries, yachts, 3 masted schooners, gulls, waves, even a dolphin maybe! This great photo album - https://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ shows a daytrip in June ... if u go july/august make it on a weekday or 2 (Athenians flood the place on weekends) Aegina has a few nice beaches, this cafe - http://www.aeginagreece.com/aegina/pages/beaches/la_palma_marathonas_cafe_bar_restaurant.html has a nice little building just back from the sands, with apts for an overnight ... you can taxi or Greenline from Athens in AM, get a ferry, enjoy sightseeing (Aegina has the BEST-preserved Temple of any Greek Isle), beachy afternoon & sunset, then back the next day.

In Peloponnese in August, yes, there are crowds, but they concentrate on certain beaches and "resorts" (package holidays) like Stoupa, Kalamata, on west coast, and near Nafplio, Tolo. But there are great little nooks I and others have found --

• ASSINE - outside of Nafpio, Just "around the corner" from Crowded tolo, is the little cove of Assine -- nobody knows its there, a lovely ruin, a cute little taverna. a tiny beach beside it and beyond the ruin a sandy beach almos unoccupied because no facilities... just a few places to stay -- this one right by the sea - https://www.porto-assini.gr/en-us/rooms -- and this one, about 100 yards or so from the cove - http://www.travel-library.com/accommodations/europe/greece/drepano/christina_apartments.html

• GIALOVA -- This is my secret Eden... just north of Pylos on west coast... the little village is really a strip about a few hundred yards long, about 7 - 8 tavernas a few shops, really only ONE place to stay, called Zoe Resorts (but that's a name change, its just a really nice family-run place) -- has apts by the pool, and a lovely grove of palms in front, by the beach ... divine teal-blue water you can walk a mile up the beach, only other place is a "camping" village http://www.zoeresort.com/ -- it's not the bargain it once was, but still very low-key and absolute bliss. But yo MUST resrve early, don't dither, it may already be full for August. good Luck! PS: the palm grove has basket chairs where retired Brits sit, reading 19th century novels. Your mom will love it.

Although the second option sounds way better, going to Mykonos in August will cost you a lot of time and money.
I suggest going to Peloponnese area and maybe you will come back another day to visit the rest of the islands.
Greece is worth going there every summer. Different islands, different experiences.

Sorry, but I’m going to have to correct Janet’s statement about Hydra having no beaches as we spent an entire afternoon at a lovely beach. I can’t remember the name of it, but it’s a rocky beach at the other end of the island from the harbor. We loved Hydra!

Apologies, i should have said no sandy beaches, at least accessible from harbor area.

Apologies, i should have said no sandy beaches, at least accessible from harbor area.... and "the other end of the island" may be a long hike for pre-schoolers.