I've flown out of Palm Springs, CA a few times. There are several rental outfits there - the town itself is a nice spot to be and has a choice of variously prices places to stay. Everything's close enough together that you can either walk, or just use a short cheap taxi ride. All the FBOs there seem to look after their aeroplanes well, always have instructors on hand, and you're far enough from the LA Basin to avoid most of the nasty airspace. Lots of nice trips to be done out of there and consistently excellent weather (just take lots of water, and get used to doing density altitude calculations).
Getting there from the UK, there are various connecting flights into Palm Springs international that are reasonably affordable - it also avoids the joys of LAX.
As for getting a US licence - just google "14 CFR 61.75" and you'll find all the answers. Or just search in the private flying section of PPrune - that particular topic gets discussed regularly and you should find all the answers very easily.
Last edited by Genghis the Engineer; 22nd Oct 2013 at 15:03.