40th Street between Park and Lexington Avenues, the Bedford is in the heart of midtown Manhattan, in the quiet Murray Hill area
Just for the sake of full disclosure, Murray Hill is not in "the heart of midtown." (40th/Park is a good location though -- very close to Grand Central, so you can get on any subway you need.)
Citysearch also has a Budget Lodgings page that might be worth checking out (just make sure to check the addresses, as some of theirs are in NJ.)