I think it's going to be hard to stay within that budget going anywhere far off except Europe. February fares to the warmer destinations will be high then, but European fares are at their lowest.

There's something to be said for going to some of the standard European major sightseeing cities then. The tourists will be gone, so the atmosphere will be less frenzied and more authentic, museums will be uncrowded, and in many places there will be more of a cultural "season" going on in the winter.
And often hotels will be much cheaper.

If it were me I'd think of either Paris -- plenty to do inside, and it usually doesn't get horribly cold in the winter -- or Northern Italy, since you could see Venice, Florence, etc. without the mobs. I'm not sure if those are far enough away from you though.