We are planning a trip to Dubrovnik for July 2014. We are planning on staying in Dubrovnik and taking day trips to Lokrum, Elafiti Islands, and Korcula. How many days would you recommend staying there in order to see all of these places? Is it possible to see Korcula on a day trip and the Elafiti Islands? Thank you for the help.

The Elafiti are no problem.
As to Korcula, i'ts about 3 hrs OW by catamaran (not daily) or bus. You will arrive there between 11am and 1pm (according to the day) and will have to leave between 3.30 and 4pm.
In this time frame, you can just have lunch and visit the town of Korcula, but not much more of this beautiful Island.

The Elafiti islands are a day trip in themselves.

by Korcula, do you mean Korcula town or the island itself?

You'd need another full day whatever you mean, though if you take a boat you'd only get to see Korcula town and even then wouldn't have much time there to explore and have lunch.

Best way would be to rent a car and either drive yourself to Orebic and then get the foot ferry, or take the car ferry across and drive around a bit. If you left Dubrovnik quite early, before 9am, you might get to see a bit more. The Peljesac Peninsula is quite spectacular to drive, and the road isn't difficult.

Lokrum you can do in a half day, though if you want to swim in the little inland pool and have a leisurely lunch/ However in July it will be hot and you may not want to rush around the island. Personally I'd allow a full day as well.

Dubrovnik is so crowded with cruise ship passengers during the day it is nice to get out of town during the daytime. But do allow yourself enough time in this wonderful city to see everything it has to offer. Walks the walls early in the morning when they open, before the crowds get up there, and while it is still relatively cool.

Have a great time.

For my interests, I was satisfied with 1.5 days for Dubrovnik itself and 1/2 day for Lokrum - but it depends on what you want to see and do. I didn't go to the Elafiti Islands. I spent overnight in Korcula and was glad I did, in part because I timed it to catch one of the performances of the moresca, which I enjoyed immensely. I would not have been satisfied with the limited time available in Korcula that would be available when trying to see it as a day trip.

Enjoy!

we had three nights in dubrovnik..stayed in the old town itself in an apartment we got when we drove in...from the tourist centre in the main st of the old walled area

great time
we did do a day trip out to kotor in montenegro

Elafiti yes, Korcula too far (4 hours by road, not sure how long catamaran takes or the sailing schedule).
Lokrum is just a few hours kind of thing.
If you tell us how many days you have and your full itinerary, we can suggest ways to sort it out where you can visit Korcula as well.