I think if you're only spending $200 for a Saturday night in October, you have three basic choices:
1. A pretty dodgy hostel or low-end hotel in Manhattan. Given your wants, about the best deal that comes up on Hotels.com is $199 for the Hotel Alexander on W 94th, and that is really basic (1.5* rating).
2. A slightly less dodgy hotel out by JFK or LGA (say, a Ramada or Comfort Inn), and take the train into Manhattan.
3. A pretty nice place in New Jersey, and take the bus or train in. The Hilton Newark, for example, can be had for much less than $200, and it's steps away from the train into midtown, which only takes a few minutes.
PS. Kate Canuck is right: if using Priceline, don't bid less than 4*. I would not be optimistic about seeing more PL inventory closer to October unless the economy really, totally collapsed in the next 60 days.