Where can you stay at Niagra falls ,U.S.side and not be far from the border?

Answer 1

You can stay right at the "Days Inn at the Falls" or at the "Falls Side Hotel". Both are located right in Niagara Falls, NY and both are very close to the Rainbow Bridge boarder crossing. The Rainbow Bridge is only 2-3 blocks from the "Days Inn at the Falls" and you can walk to the bridge (pedestrians can walk across) into Niagara Falls, Canada or you can drive across of course. Pedestrians have their own walking area to do so and you can view part of the Falls when walking across. It's free to walk across from the U.S side but will cost .50 cents to cross from the Canadian side back into the U.S. (I'm not sure how much it is when you drive across, probably a couple dollars).
Additionally, if you won't be driving and will be taking a bus, buses (such as Greyhound and CoachUSA or CoachCanada) only cross at the Peace Bridge (boarder crossing) near Buffalo. Regular line buses do not cross at the Rainbow Bridge at all, however I believe that tour buses do.
Take care.

Answer 2

Anywhere you stay in Niagara Falls, NY, is not far from the border. The whole town sits on the border, which is the Niagara River.