We stayed at the Red Roof Inn (don't laugh - it was nice) ... Midtown, right across the street from the Empire State Building. It's in your price range and a great location. If I were you, I'd try to be closer to Penn Station than Grand Central. Much of the things we're interested in doing in Manhattan are closer to that part of the island. Grand Central can be really out of the way and add a lot of walking to your day.
You could also try Priceline, we got a Best Western and a well-reviewed suite hotel in Midtown near where we want to be for $130 a night in the middle of the summer.
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