Fishing, riding etc in America..help

Hi
I'm thinking about popping over to America with the family. Fancy a bit of
trout fishing and general "get away from it all".
Quite like the idea of going off on horseback for a few days. I prefer river
fishing on the smaller rivers, chalk stream and spate.
Found this site which seems to be the sort of thing I've in mind
http://www.utrail.com/index.html.
Now my geography is bad but I do know that the USA is bigger than Britian.
So any idea's on how to narrow it down? Books etc? Suppose a few days in
Montanna is a "must do".Fire hole? Not into cities....OK yes if there are
good tackle shops:-).
Other thoughts..Gators, bears, swamps and lots of lovely land with not a
town in sight.
Any pointers on this rather broad question appreciated.
B Bear