I'm sorry to hear that your plans have taken on the shape of a pear! I went to AAA several years ago but am unable to recommend them.
I hope you are able to change schools but by not going to AAA you're avoiding the worst of the wx....San Diego suffers from the "May grey or the June gloom" so you would have been sitting on the ground a lot anyway. It is a nice city and well worth a visit, but not necessarily for your PPL at this time of year.
I wouldn't worry about FL not being that "nice" - it is fine. You're there anyway to do your PPL not go sightseeing! It is low lying too so any low level stratus needn't be a huge problem. I would definately go for the US - it is going to be cheaper than the UK and the Americans embrace GA while in the UK it is merely tolerated.
Good luck with your PPL!! PM me if you would like some more info on CA vs FL....I've done both.