San Diego is of course a must see. I prefer the Safari Park (the new tiger complex is amazing), but if you want to tick off lots of rarities then the zoo is the place. Florida also has some of my favorite zoos (and some good scenery as well), so you will certainly have a fantastic time here in the states.
Not being able to do the San Diego set is frustrating, yet I have to offset that with the fact that a work trip got me out here and I get to visit the world renowned San Diego Zoo at all
Safari Park next time.. and AZ!
I'm up on the Florida Panhandle this time and there is a dearth up there. I've done Central Fl before and yes, I loved it.
Not sure how far you will be from Jacksonville, but if it is within reach it is a very good zoo. I visited in January this year (also on a work trip) and was duly impressed. Of course you will also do well just visiting a swamp in your area. Very unlike the British countryside I am sure!