Shem the Penman said:
I'd say NYC, but that doesn't fall in the "not be bankrupted" part -- you might be able to find a berth in a youth hostel, but even so NYC ain't cheap. Perhaps Washington, DC, which has no shortage of sights to see.
I grew up just outside of D.C., and it's a damn good choice. For one thing, the METRO (subway) is cheep, clean and safe. A great way to get around town and the suburbs. In fact, it's worth seeing all on its own! It hooks up with the bus transport system.
Be sure and visit the Smithsoneon. Last I knew there were over 20 buildings in the complex, not to mention the national zoo. Entrance is free (tours may cost something). My favorites are the Air & Space Museum and the Museum of Natural History. There are also two art museums, one for modern art, the other for more conventional stuff. The Imax theater is also a great thing, but it does cost a few bucks.
If you've ever served in the military, the Changing of the Guard at the Tomb of the Unknown Soldier (Arlington Cemetary) will bring a lump to your throat, and swell your chest with pride. Even if you've never served, it's an impressive display.
Lodging may not be all that cheap. If it were me I'd try to get reservations from one of the on-line discount motel services.
Now, you may be asking yourself... if I'm so thrilled with D.C. how come I no longer live there? The answer is that it's a great place to visit, but I wouldn't want to live there!
😀