I took a road trip around the southern part of Iceland last year. Shorter flight from Boston to there then to the West Coast of the US. But it felt like I was on another planet with the extreme and exotic scenery. The people were very friendly, the dollar is actually worth something over there, and the food....er, let's just say I didn't gain any weight on that vacation. Try the hakarl!
The best place for just a new experience -- Denver. I first went there in 2002, traveling across the country via Amtrak with my best friend, as a graduation gift. (My friend didn't find the sleeper car quarters as ... charming as I did.) Denver is such an odd duck of a city, even within a 16-block radius you can find distinctly different neighborhoods.
I've road tripped cross country and regionally a few times. I've always wanted to do the train thing though. The dynamic has to be so much different than driving on the Interstate. Denver is a quirky place, though about all I did there was take in a Rockies game. If you want odd duck, try Boulder. It's like a Rocky Mountain version of Burlington, except the mountains are higher, and so are the residents.