Hey... that sounds like an awesome ride... good luck with it.
Do you have an image for which states you would be riding through?
No disrespect to any of my neighbors, but some places in the US are more interesting for motorcycles than others.... and different bikes are better suited to different regions (west cost, mountains (rockies and apalachian), central plains, etc...).
A 250cc street bike would be a blast for New England, Southeastern US, or the West Coast (slower speed limits and twisty fun roads)... it would by MUCH less fun in the grain belt (higher speed limits (70 or 75 MPH) and straighter roads...
Also, Getting up and over the mountains in the east and the west will require a bit of power.
I've ridden a Vstrom 650 most of the way across the country 4 times, and it has been the perfect bike... fun in the twisties, not too uncomfotable doing 90 MPH through Nebraska (sorry to my Nebraskan friends, but I really neaded to get back to Detroit, so I sped though your homes).
Still, it's almost 500 lbs wet. If you want light, a KLR 650 is a good choice (as mentioned earlier), but can be a little bit twitchy at higher speeds.
As somone else said, get what will make you happy, and a 250 is doable, just maybe not the most comfortable for long days in the saddle (to give you some perspective, it's about 4,500 km from New York City to Los Angeles... by expressway).
Anyway, what ever you pick, if you're in Minnesotta, drop me a note, and I'll treat ya to a cool beverage to help you on the way
Safe riding!