In reply to Paps85:
In terms of the wilderness experience,I would certainly like to go back to the Wind River Mountains in Wyoming.It may not have the most intense climbing,but it is such an expanse of untouched land and just beautiful.You could perhaps do it the other way round and go to Jackson Hole and team up with someone climbing out of there.Then you could head into the Wind Rivers with your new climbing friends.
I also like the cascade mountains in Washington state and then of course there is Alaska.
All of the above is more in the Alpine style and for more uniformly typical rock climbing you would have to go to somewhere like Smith Rocks in Oregan(not been there)or consider some of the insane crack climbing in Utah(doesn't appeal to me).
The suggestion to go on to a parallel site to this in the US is another suggestion I would give as mentioned in the previous reply.
Whatever you do, Good Luck.It will be fun.
Rob