Gas, lodging, and food can eat up a budget pretty fast, but.....My wife and I plan all of our trips around National Parks. They re generally inexpensive to visit and there s a wide variety of natural, historic, and cultural sites. You can pick up a National Parks Passport (a little book with a map and places to record free stamps with the date of each visit to a NP) for about 8 bucks and keep a record of all your journeys together. My wife and I bought one right before we got married and have been collecting memories for almost 15 years, including our honeymoon in Hawaii (7 parks), our 10th anniversary (Dry Tortugas NP off Key West), and numerous family vacations. We have Passports for each of our kids now too, so they can collect their own memories! There are plenty of places you could check out within a day or two drive (or Amtrak ride) of NYC. (Washington DC might be a good place to consider.)
I don t know nice winter vacation places on the East Coast. However, check hostels. If you re a student you get a great rate. I ve stayed at one in Yosemite and San Diego. The atmosphere is fun and breakfast is usually included. You share a bathroom. I enjoyed visiting Branson, MO. I liked driving the woodie go cart. There s lots of shows to see.