In reply to Stairclimber:
We climbed on Hvar in 2015 and 2017, both times in early May and as part of a week long loop around Split, Omis, and Hvar. Really enjoyed both trips.
Cliffbase is cool, and as mad as it seems from the descriptions (including a smugglers beach and wine cave / cellar), we had the little "apartment" there which has two double beds and was comfy for 2 couples. Lots of routes, we climb in the 5+ to 7a range and barely scratched the surface with 2 days climbing. It's a 30 minute walk in and a bit isolated.
We stayed in an apartment in Hvar town which is very different, lots of cool restaurants etc. and most of the climbing is a shortish drive. My understanding is that Hvar becomes a big party town in the summer so worth considering if that's a good or bad thing!
I'd definitely hire a car.
If you're not set on Hvar, it might be worth taking a look at Omis to see if it fits what you're after. There's a beach and plenty of climbing.