I've been to Korcula twice, both times in the summer of 2004, my parents have been back several times since. Whilst the Istrian Isles are pre-dominately visited by Germans, Austrians and Dutch, it seems that the Dalmatian ones are more popular with the Brits, Hungarians, Czechs, Poles, Italians and Croatians themselves.
Korcula is a fine looking island about 50km long and only 1km away from the Peljesac peninsula. Originally inhabited by Greeks who called it Black Corfu, it was then Slavs and Venetians who took their place it then changed hands so many times that it's complicated to keep hold of (Serbs, Venetians, Hungarians, Austrians, French, Montenegrins and Italians all had a part in the history of this island)
Korcula like most of the Croatian Islands is very seasonal, the season starts in May and goes on until the end of September, outside of this season, you can expect to find many things closed.
As well as having the usual array of watersports and boat trips, there is also the possibility of scuba diving in what is most probably one of the Adriatic's diving hotspots.
I've never stayed in a hotel there, I've only used the campsite, which is fine even if the ground is a bit too hard. I wouldn't be able to tell you much about hotels there but there is always the possibility of renting a room from one of the many of tours. The price is forever changing, it was around 10 euros per person 4 years ago but I'm sure it's higher now.
If you are basing your holiday in Korcula, trips can be made to Dubrovnik, Hvar, Vela Luka, Orebic and even Mostar in Bosnia. If you are just going there en-route to somewhere else, you will be glad to know that it's well connected by boat to Split, Dubrovnik and Hvar and by bus to Zagreb and Dubrovnik.
Picena Cove which can only be accessed by foot, comes highly recommended as a beach. Ask locals for directions.
The nightlife tends to rather focus around the square and Fresh bar is a good place to start, they serve up tasty wraps and great shakes to get rid of hangovers! Sangria in plant pots is also a speciality and comes highly recommended by me! By night time, liveliness gets going and they will inform you what is happening in the town that night and where the place to be is!
As beautiful as Korcula is, there is actually very little to do.. this makes it the perfect place to relax but it's not the kind of place you'd go sightseeing. The food is generally of good quality in each place and the ice cream is superb (it's great everywhere in Croatia actually!)
Their most famous explorer is the great Marco Polo, he's the most famous person from the island and this becomes an over-used marketing aspect! Marco Polo hotel, marco polo restaurant and so on!