£1900 is nearly $3000, plenty to purchase a solid used motorcycle here. And to echo TA's sentiments, that's more than I spent riding 30 days and 6600 miles from the east coast (Maryland) to Alaska this past March. And I wasn't being particularly stingy about hotels or food. Unsure how you would go about titling, registering, and insuring a vehicle bought here but I imagine it can and has been done. There's nothing quite like bringing your bike with you of course... I believe I've seen it may be cheaper to ship to and from Canada though; Toronto seems to stick in my head for some reason. Not terribly far from NYC either, 500 miles or so direct.
Gas prices have been rising. Still cheaper than Europe, but its a big
country. I saw prices ranging from $4.00-4.50 a gallon for regular, about $0.20-50 higher for premium this spring when I crossed and moved up to Alaska. This will probably be the summer it hits and stays over $5.00/gal. So, one place to save fuel is a more fuel efficient bike whether you buy it here or bring it over.
Camping will be much less expensive than staying in hotels, especially since it seems that cheap hotels are fast disappearing. It was rare to find a place even at an old mom n' pop motel for less than $50/night before taxes. Most campgrounds near population centers are anywhere from $10-35/night. Many National Forest, BLM, and National Park as well as many state and local camgrounds are free or nearly so in the more remote areas. A lot of the pay sites have access to water and showers, some even have laundry. Most of the free camping is west of the Mississippi River. You could always investigate websites like couchsurfing.org or this forum for houses to stay for nothing.
Food can be another budget breaker of course. Good local diners and cafes will often have decent to good food at prices equivalent or better than the chains, so support the little guys. Liquor laws and prices vary wildly from state to state and county to county in some states. You could easily save a bundle by buying fresh food and cooking for yourself as you go, but there's a helluva lot of good eatin' out there.
If you plan to visit a bunch of National Parks, or even just a couple of the big ones with hefty entry fee's, it might be worth buying an Annual Pass (I think non-US citizens/residents can buy it).
U.S. National Park ServiceAmerica the Beautiful – The National Parks and Federal Recreation Lands Pass Series
2008 Yamaha WR250R