Hi Carolyn, I was in Croatia last June and I would pick Korcula over Hvar. Korcula has a more unique feel to it and is more quiet at night. Hvar has more of a nightlife but you can have that in Dubrovnik. too. If you are in Korcula I'm not sure I'd do a day trip to Hvar because of limited boat schedule and time but that is up to you. We stayed in Sobe Tedeschi and the owners were fantastic and the room was great and had a view. We could also walk out the door and and across the walkway to the stairs down to the water and go swimming.
In Dubrovnik we stayed in Sobe Renata and it was easily one of the best places we have ever stayed in (and we have stayed in a lot of nice places). We had the top room which is one of the highest points in town and we overlooked the harbor. At night we were serenaded by the piano bar below and could see much of the happenings from our room. The room was large and had all the ameniites for a very good price.
Both places are in the RS quidebook but we did check out his other recommendations while we were there for future trip plans and they were nice also.
You'll love Croatia