in the 3-4k range youre looking for something a little older.
maybe check out this article for some ideas and then look for specific bikes:
Comparison Test - 10 Sport-Touring Motorcycles - Popular Mechanics
you for sure will be uncomfortable on a sport bike for 250 miles. i never like riding a sport bike for more than an hour or so before i get a sore ass. a yamaha FZ1 might be right up your alley. i always thought an FJR1300 would be an awesome bike without those stupid saddle bags.