Need Itinerary Help! Croatia, Italy, Greece

If you want a somewhat relaxed trip, choose either Greece or Italy for spending most of your time. I know more about Italy, so will suggest flying from Dubrovnik to Venice and working your way down the country, staying 3-4 nights each place. There is plenty to do and see in Italy. You could fly home from Rome or Naples. You could go from Venice to Florence, then on to Sorrento for a change of pace and to relax on the Amalfi Coast or Capri. Returning to Naples and Rome, you could spend time in Pompeii or Herculanium.

Start by searching open-jaw flights from your home, for example into Dubrovnik and out of Athens (you would fly or ferry from Italy). There is no way for anyone to answer this for you until you do some of the initial legwork of looking at the affordability and convenience of flights based on your specific needs.
If you really want relaxation, I would consider dropping Greece. A month would allow you to very leisurely and extensively explore those places in Italy and Croatia, without spending any additional times in airports, etc. It is doable to include Greece, but I think you will have to scale back. Remember moving more adds expense, too.
Also, though it might make sense to do each country in one block (getting immersed in food/language), since you want to start in Dbv and end on a chill note, a good circular route might be the following:
Dubrovnik, ferry to Bari, Amalfi Coast, Rome, Florence, Venice, into Croatia and back down the coast--especially if you get a good deal on a round trip to Dbv, this would be great. There are just too many options to consider at this point.
ps letting us know what month is very important. have fun planning!

I recommend that you fly between the countries, no matter which order. From Dubrovnik, you can get good flight prices to either Rome or Athens but will probably have fewer choices to Venice; try www.skyscanner.com. There are also overnight ferries (not all everyday) to and from Italy, but no practical ferry, train, or bus from Croatia to Greece.

Wow thank you so much for the responses! This trip came up really quickly, we're actually leaving in three weeks for a mid-August to mid-September trip (so we're mentally prepared for LOTS of fellow tourists). This is also why I'm not ready to ditch Greece since I really like the idea of mixing in big cities with quieter island trips (I've heard Peloponnese in general is on the less touristy side compared to Mikonos etc.)

I was also considering looping around from Croatia to Italy back to Croatia then Greece so I'm glad to hear that doesn't sound nuts! I have a lot of flight comparison to do today. FYI, if anyone's interested, this website occasionally has super deals for flights between smaller cities in the area http://www.volotea.com/en <--- if I can find the right route this might help narrow it down!

Also, curious if anyone has rented a car in any of these areas? We love driving and road trips so I can imagine cruising around Amalfi coast would be gorgeous but I'm not sure about Croatia... thoughts?

You don't want to drive on the AC--not in August, maybe in late September it would be okay. There is so much traffic and parking is exorbitant. There are buses and ferries (shoot for the ferries over the overcrowded buses).
In Croatia, driving is a breeze, but make sure your rental is allowed on ferries. The public transport is really quite good in Croatia. If you skip the car, you can make use of catamarans, which are running on a high season schedule in August. Once you get your itinerary set, I can advise on getting around. I visited several times with no car. I prefer cars for day trips on the islands (or if you weer in the interior, would need one there).
If Greece is a must, then you'll have to rush through the others. Just write it all out day-by-day once you get some air travel ideas more sketched out. good luck!

There are plenty of islands to choose from in Croatia - you don't need to go to Greece for this. To use your own words, squeezing Greece into your itinerary is nuts! The only place in Greece you can fly to from Croatia is Athens and this is a hideous airport in summer.

Visit Brac, Hvar or Korcula instead of Greece. Better food, good weather and a better chance of finding accommodation for peak season so late in the day. Bookings for Greece are high this year from Europeans seeking to avoid Turkey, Tunisia etc.

A fairly brisk pace is 2 weeks to cover the Croatian element alone, from the north down to Dubrovnik. Ideally, this element is a 3 week holiday. There is lots to see. Istria needs a minimum of a week. Plitvice and Krka national parks, Split and Trogir, the islands and Dubrovnik. Croatia is much better value than Italy. Decent public transport too.