Honestly, it kind of doesn't matter that much. There are some sketchier hotels in some grubbier areas but they'll be oddly priced and clearly not mainstream hotel type deals. Manhattan is 10 miles long and about 3 miles wide; hence it doesn't matter so much, you're pretty close to anyplace and if you stay in a neighbourhood well, bonus you get to see the neighbourhood.
I'd personally stay out of Times Square and not do the Financial District. Too much crap at the first, nothing at the second. Oh and do not stay at the Hotel Pennsylvania on 7th. They may have deals, you do not want them. Aside from that...

There are a lot of hotels here.
I don't know what they're charging for Labour Day wknd at all but in general hotels that are nice or decent and you may find a deal (and there are plenty I'm not mentioning/thinking of, etc) - The Library Hotel is lovely, the Sheraton on Seventh is a big honking Sheraton that sometimes has deals, the On The Ave on the Upper West Side is very nice, there are a bunch of boutiquey places on the lower end of midtown...a new thing with funky lights I can't recall the name of but maybe someone else can, in the 30s, and that place with the pool...not the Gansevoort. The Gansevoort is plenty nice, I'd just wager they'll be out of your price range but can't hurt to look.
Oh, there's also the New Yorker, on 8th and 33rd, that's decent and may be reasonably priced.
If there's something you've found that has a decent-looking deal, post the name/location. Chances are someone either knows of it or will know based on the location.