Consider Toyota Corolla and Camry if you know they aren't afflicted by the "engine sludge" problem. They share with the Honda the need for regular changes of the timing belt, and the water pump as long as you're in there, but also its reliability and frugal fuel consumption. Nissan Altima and the recent, nicer years of Sentra might be worth considering -- a '95 Altima that just recently left the family will probably be driven by the three-foot mutant cockroaches that inherit the earth after nuclear holocaust.
Subarus are great for winter and are very practical and well thought out cars in general, but you'll be hard pressed to get a good one for $3k and a bad one would be an expensive torment to you -- they have several potentially expensive failure modes that call for diligent preventive maintenance and avoidance of certain operating practices, so they have to be evaluated *very* carefully on the used market (but a good one, well cared for, will last and last and last). They aren't the best on gas mileage either, in their classes.
Among tolerably recent domestic models, the Chevy Cavalier is a comparable model. I used to get them as cheap rental cars quite often. They don't inspire or reward performance driving but are decent on gas, and one that a friend of mine owned served her very well until its last act, which was giving its life to let her walk away from a T-bone accident.
Another consideration: Does she drive a stick (and, if New York will be the actual site of the car's use, does she want to?)
Best of luck,
--Joe