I guess you can rent a car (about $25-30/day) with international driver`s license. Then you can go around when you take the day off:
Norfolk: There is bus from Williamsburg (where Bush Garden locates) to Norfolk, but it take time. If you drive by yourself, it`s about 25 miles and half an hour
Virginia beach: from Norfolk, another 0.5 hour`s driving
Richmond: 2 hour`s driving from Williamsburg. Pretty nice old town. But becareful of some neiborhood.
Washington DC: from Richmond, another 3 hour`s driving. you can also take Amtrak train from Newport news to DC, it`s about $70 and 3.5hour, then you can go to Philadelphia (2.5 Hour) or Newyork (5-6 Hour)
I think Hampton Roads (including Williamsburg, VA beach, Norfolk, etc) is a good place to visit and live. It`s not exciting or convenient as NY but you should have fun there. The weather is great there, too.