10 day trip to Croatia in May 2018 recommended itinerary

Airport choice depends where you choose to go in Croatia. Most seem to head south toward Dubrovnik and the Dalmatian Coast, but not everyone does.

If you don't want rushed, stick to Split, Dubrovnik, and an island like Korcula or Hvar - though May is just the start of their season so I'm not sure how lively the islands will be yet. In that case, try to fly into Dubrovnik, out of Split, or vice versa.

If you want to do northern Croatia (Istria, Plitvice Lakes, Zagreb) then Zagreb is probably one of your airports. Venice could work for the other to get to/from Istria.

Try Booking.com for accommodations. In some parts of Croatia, you won't find many proper hotels - apartments and sobe (private rooms probably with private bathrooms) will be your best options. Both will come up on Booking.com. Check AirBnB as well if you wish, could give you better choices in some places. Many properties on Booking.com offer free cancellation up to a cut-off date which is handy if your plans change.

Good advice from Andrew.

I was in Croatia in May of 2014 and spent two night each on Hvar and Korcula. It was not yet peak season, but not dead by any means. It was nice that the crowds were smaller. One day on Hvar I hired a young fellow with a boat to give me an hour tour. In peak season these guys would be too busy ferrying passengers back and forth to nearby islands to do that.

One thing to consider if you decide on Split and Dubrovnik plus one of the islands: you won't really need a car for this itinerary, unless you want to rent for a day trip (say to Mostar or Montenegro). But you can travel between these destinations easily without a car. If you choose a more northern itinerary, a car would be more useful. But be sure to check into dropoff fees if you start in Zagreb and and in Venice; they can be very high for dropoff in a different country.

Another option would be to fly into Zagreb and end in Dubrovnik, but then you would probably not have much time to visit the islands. Something like this would work (assuming 9 nights):

2 nights Zagreb
1 night Plitvice (spend the night and then visit the park first thing the next morning)
3 nights Split or Trogir (possible day trip to Hvar)
3 nights Dubrovnik (possible day trip to Mostar or Kotor or Cavtat)

Whatever you decide, you are sure to enjoy your visit to this beautiful country!

It's best to start with some reading--narrow down your choices so you don't get a dozen random itineraries, all different and having nothing to do with your interests. At the very least north or south.
Late May is the only option for swimming unless you can handle very chilly seas.
Step two should be to search flights from where ever it is you are coming from. It isn't the cheapest/easiest place to get to with limited time.
Car is unnecessary for most typical first time itineraries, as the towns are well connected by bus and ferries. If you rent a car, then make the most of it and stay off the beaten path entirely. But, with four people you might find it just as easy with a car--however, then you have to contend with parking and you will need to pack light to fit luggage.
They practically invented airbnb--apartment rental has long been the norm in Croatia and is a fantastic deal.

I go with Lane's itinerary. We have been to Croatia 4 times since 2011. There are lots of worthwhile sights, but he suggests the best. I will mention that if you stay in Split for 3 days, Trogir is a nice day trip on a boat - 2 hrs to Trogir, 5 hours in that small city, 2 hrs back. Very pleasant trip. I don't see 3 days in Trogir - it's very small.