I posted on a similar subject a while back for a great flying holiday I took in Florida.
The US Embassy in London was very cagey about whether or not I needed a visa. Since I wasn't planning on training for a new license or rating they told me that technically I didn't need a visa. However (and this is the incredible bit, bearing in mind they are supposed to be the last word on this), the final call is down to the immigration officer who can be having an off day and might give you hassle or refuse you entry altogether.
Getting the visa I "needed" would have cost the best part of £100 and required a half day of standing around at the Embassy. Consequently I decided against the visa - and had no trouble at all. I didn't exactly draw attention to the fact that I was planning on doing some flying, they didn't ask me so I didn't tell.
Re the actual flying bit, getting an FAA license on the basis of your UK PPL is easy, as you need only to fill in the security forms from the FAA and the CAA, pick up your license and then do a BFR. Note that you should officially allow 60 days prior to your trip to get the paperwork through (its posted to you), but in general the process a matter of days for the CAA (this is according to the nice folks in Oklahama what I spoke to).
Have fun!
