Personally I'd recommend North Carolina or Oregon (the Columbia river valley)
Where do most Americans go for holidays?
Usually to some other place in the US, but the most common other countries would be Canada, and Mexico, just because they are easy to get to. After that, the Caribbean and Europe.
What do you like? I personally like backpacking (trekking), so places that I like are the Sierra Nevada Mountain Range in California (which has Yosemite, Sequoia, King's Canyon, Mount Whitney - the highest mountain in the continental U.S., etc.), Yellowstone, Oregon (ocalhoun suggested North Carolina... I've never been there but I'd imagine that it's nice), and Minnesota (which is near Canada - which is really nice.) Florida has nice beaches, and it has the Everglades (really nice). If you like the touristy city scenes, then Southern California (where I currently am at - and hate). Southern California has San Diego - an amazing city. It also has Los Angeles county, which has places like Hollywood. Palm Springs is a popular destination (although I still can't figure out why). New York City is a popular destination, although there's a little too much site seeing and not enough "doing" for my taste. If you can make it down to Nevada, you can drop by Las Vegas, which is one of the funnest cities that I've ever been to.
Americans usually travel to places in the United States. Many Americans are workaholics (or short sited about other countries) and do not get out of America much. When Americans do, they go to Mexico and Canada frequently, because like ocalhoun said, it's easy to travel there (passports are just now becoming a travel requirement to those two countries.) Americans also like to travel to the Caribbean (The Bahamas is popular). After that I'd have to say that Europe is the next traveled to place. France, Spain, Germany, and the U.K. tend to be popular here. The next most traveled place is probably Asia, then South America, and then maybe Africa. That's just a guess - I don't know the statistics.
This is just a person desire, but I would go to either Japan or Australia for my next big adventure. I have been to Germany already and loved it. I have a certain fascination with Asia and would like to spend some time in Japan and see a new culture. Australia or New Zealand is also appealing to me.
U.S.A. is probably a good call, especially now. The dollar is weak and everything will be cheaper.
But, the U.S.A. is a very big place. I don't know what you like to see and there is probably something for everyone in some part of the U.S.A.
If you care about your budget, go to the South. The prices are lower in this part of the country. One of the nicest natural areas is the Great Smoky Mountains Natural Park, and you can also go to the beaches in the Carolinas or Florida. The South also has a reputation for hospitality.
If you like cities, there is none like New York. However, Boston, San Francisco, Philadelphia, Chicago and Washington D.C. are nice too.
The U.S. has a strong british influence but it is also a very multi-cultural society. You can see either of these aspects depending on where you choose to go.
Hope this helps.
Two countries I would like to go back to would be Thailand and New Zealand.
They were both very pretty and have very freindly people.
Well my mom is from England, and my father from the US so, although we live in the US, we visit the UK on a regular basis. I know plenty of brits that love coming to North Carolina (where I live). In NC there is something for everyone. We have mountains and beaches, golf courses, shopping malls, big cities and little towns.
If I could visit anywhere, it would probably be Western Australia again to visit my Uncle.