Travel by train, ferry and bus tips and hotel bookings?

Hi Allie, Welcome to the forum. A couple websites to look up ferry schedules and fares are: www.Ferries.gr
and www.Ferryhopper.com
The boat trip to Santorini from Piraeus takes anywhere from 5 hours to 9 hours and costs from $59 and up. Flights bought well in advance cost less and you can see what fares are like at www.Skyscanner.com
There is some pricing variation between ferry companies but it’s not imperative to book ferries ahead of time for travel during September.. I would wing it, because that is part of the fun of traveling in Greece when you have the time to slow down. I usually buy ferry tickets at the port the day before the ship sails.
The Greek train system never was developed with an extensive high-speed network and so taking trains can seem painfully slow if you’ve traveled before on a high-speed train.. You might find the trains part of the adventure with a month to travel. You don’t need that much time to cover your destinations, but with even two weeks—- you have time to get in sync with Greece.

While the trains in Greece are no way to do a blitz tour of the country—-they will get you to Olympia. To get to Olympia from Athens you first go to Pirgos where you change to a train that continues to Olympia. The journey takes about 4 hours total so plan to overnight in Olympia. To really get in sync we th Greece, stay in Olympia two nights. Nafplio, Mycenae and Delphi are best visited by bus; Nafplio takes about two hours from Athens and Delphi takes about three. In the U.S., we tend to think of Greyhound when we think about buses. In Europe, the buses are far more comfortable and much cleaner. I wouldn’t hesitate to take a bus in Greece. You can get from Nafplio to both Mycenae and Epidauros by bus in one hour. So you might plan to base yourself in Nafplio for four nights or more and daytrip to Epidauros and Mycenae.

Delphi can be reached from Athens by bus in three hours.

Without a rental car. Meteora is probably best visited as a day-trip from Athens. Trains take 5 hours to reach Kalambaka, which is just a few miles from Meteora. I’m sure www.GetYourGuide.com shows tour companies that offer tours of Meteora. Some are overnight trips that go to both Delphi and Meteora.

Have fun in Greece!

Ferries to Hydra are mostly small catamarans with no access to an outside deck. Prices range from approximately €30 to €40, depending on the company.

It's not necessary to book in advance; if you do, avoid www.ferries.gr, which is a service that will charge you a "surprise" additional fee when you pay at the end of the booking process.
Ferryhopper doesn't charge any additional fees, but the easiest way is to arrive a little early at Gate E8 at the port of Piraeus, where ferries to the Saronic Islands depart, and purchase your tickets at the ticket offices on the docks.

Regarding the mainland, given how difficult it might be to get to all the places you mention by public transportation, perhaps you should reconsider renting a car. You'll save a lot of time and can go wherever you want, whenever you want, without worrying about bus schedules and connections.

There are no particular difficulties driving in Greece. Many people on this forum who weren't keen on renting a car at first can confirm that everything went smoothly.

How far in advance is it necessary to book a hotel room?

It's up to you; the range is between booking 10 months in advance and not booking anything at all.

Since you don't yet know your exact dates you can still check out platforms like booking.com and make a list of favorites in the different places you'll be visiting.
Also, check if the hotels or accommodations have their own websites, this will save you from having to go through a third party.

Also, look on Google Maps, you'll see quite a few places not listed on the usual booking platforms.

Ditto--the driving is not difficult and will likely save you time (which IS money) in the end.
If I was going to do five weeks by public transport, I would just wing it. Or, you can book some small tours.
The Bradt Guides are really comprehensive and you might peruse one to see if there is more public transit info.

Thank you for all the information so far. I haven't seen a train that goes to Olympia only buses? If I were to consider a car (my husband isn't coming with us so it would be likely me driving), what do I need to know - car rental companies, parking, best place to pick up and drop off a care (I don't want to drive in Ahtens!) etc. Also I saw someone else post that parking in Delphi was difficult?

We picked up/dropped off the car at ATH airport. We did get an IDP just because we are used to getting one for Italy, but I believe it isn't required for Greece (for $20, would I just get one anyway? probably.) I usually go with Hertz, but Autoeurope is good for doing a comparison. Local companies seem to be recommend often for Greece, which is not the case in other countries I have visited.
I was only in the Peloponnese and did not make it to Olympia or to the north. Parking was never even the slightest consideration, even in busy little Nafplio. You could also skip Olympiaa, which I get the impression is really not all that--Messene and Nemea scratched that itch for us.
Bus travel is likely the main form of transport you will use if you skip the rental car and don't want to do a tour (I don't drive, so I absolutely get it--but only you know if you are comfortable enough driving to do it. It has nothing to do with the country--I rarely drive at home, so I don't drive on vacation. The roads I encountered were perfect--main highways were in excellent shape, and the rural roads were reliably rustic.)
Early fall should be an amazing time to be there, good luck!

There is no train line to Olympia, nor to any other place you might want to go in the Peloponnese.

There is no direct bus from Athens to Olympia; you must first take a bus to Pyrgos from the Kifissou bus station in Athens, then from Pyrgos take another bus to Olympia. If all goes well, the total bus journey will take about 7 hours. If you arrive in Pyrgos too late, you will have to stay overnight and then take a bus the next morning.

There are countless car rental companies in Greece, the usual majors like Hertz, Avis, etc., as well as plenty of local companies.
Even those without an office at the airport can arrange a pickup and drop-off at the airport.

In town, almost all of them are located in the same area, on Siggrou Avenue, here:

https://maps.app.goo.gl/xpaxEYsTKExFHqjE6

Zoom in to see more.

Wherever you go, I don't think parking will be an issue in October.

I've occasionally driven in Athens, and it's not a problem for me, but it's usually just to get in or out of the city or to stay overnight. Otherwise, it's obvious that a car in Athens for anything other than leaving or entering the city is completely unnecessary and requires some practice.

If you pickup a car at the airport you will be 2 hours 15 minutes from Nafplio via an extremely easy road, 80% highway, and without going through Athens.