The Travel Inn, which is between 8th and 9th and 42nd I think, might be 9th and 10th ave, I've seen run well under $250. It's the middle of the pack on TA, and it has a pool. Plus I'm pretty sure it has free parking as well.
We've stayed at the Millennium right behind the Good Morning America studios already, for around $200 a night. It was a very nice room, and very nice hotel, though the beds were some of the hardest things I've ever slept on. I don't think they had a pool either though.