In Dubrovnik we stayed in a terrific apartment with a stunning view of the Old City - a bit of a climb up but nothing dramatic and there are lots of buses. I considered staying in the Old City but was happy we chose the view as I never tired of it. The family who rents these apartments is lovely (and onsite if you need assistance)

http://www.dubrovnik-accommodation.net/index.html

And here are my sunset/sunrise time lapse videos - I was having fun with a new iPhone time lapse app!

http://www.youtube.com/watch?v=PVgdtx7a71w

http://www.youtube.com/watch?v=unlMsbHQmrI

How many of you are there? How much do you want to pay per night? What kind of accommodations do you want? There are many soba's available in Croatia, holiday apartments rather than hotel rooms.

Some people prefer to stay in Trogir instead of Split. It's a pretty small town that's a UNESCO World Heritage Site. There's a bus into Split (takes 30 to 50 minutes depending on whether you get the local or the express). Also Trogir's not far from the Split airport.

We stayed in Trogir (or rather just across the bridge in Ciovo) at the Villa Moretti: www.villamoretti.com. We highly recommend this place.

If you plan on renting a car to explore further afield, then it should be fine, but if you don't want to do that, then you could add one more destination. The ferry/bus schedules are quite convenient for moving along from place to place. For example, you could stay a few days in each and also add Korcula or Hvar in between. It really just depends on what you want to see/do and your travel style.
Vis is amazing--one of the most stunning places I have ever been, with some of the best beaches in Croatia. A car or scooter rental is pretty vital to see the island unless you are quite the biker/trekker. I rented my place through http://www.adria-island.org/.
General apartment rental advice: As long as you can see on a map where the apartment is located and see photos to know that it has a view, you are all set.

I should add the caveat that the beaches in Vis are pebbles (which I like) and not always super easy to get to--that is what makes them nice! Their cove-like settings also can result in litter washing in over the winter, but by June they will have done beach sweeps to clean up.

> We are traveling for 2 weeks - also interested in hearing opinions on the 3 locations we've chosen - whether we should reconsider other options.

What are your interests? Are you viewing these locations as bases for visiting other areas, and if so, which? (In 2 weeks, you can probably visit more than just these 3 places.)