An interesting thread. I, like many I know, did the FAA licences and converted to JAA. It was much cheaper than doing JAA in this country. I went from flying a Cherokee to flying an Airbus for a UK airline after training in the US. I did a conversion from FAA m/e PPL with single engine IR to CAA multi IR in under 10 hours.
As for the myth that airlines don't want pilots who've trained abroad, well, lets think about this. If you train in the UK its likely to be at a tinpot airfield with lots of training traffic. If you train in the US you are likely to get a lot of experience mixing with airline traffic, flying into major airports that airlines use, flying at all sorts of altitudes, to airports in all sorts of terrain (well perhaps not in Florida!). Once working for an airline you will spend the first 30 minutes of your day going from a very busy airport, talking to a very busy ATC, following their instructions, and getting out of the country. The rest of the day will be spent flying, yes, abroad. Hmm, I wonder what experience airlines would prefer? If you have plenty of night, instrument, cross country time in busy airspace, flying into international airports I reckon thats more relevant than doing 50 circuits at a grass strip.
As for flying in the USA, I have flown all over and although Florida is OK, you will get bored very very quickly if you are hour building. California has a great variety of airspace, airports and terrain and you will learn loads. Alternatively you could train in Florida then hire a plane and fly across to California, gaining experience of the different states on the way.