I am thinking about possibly aithger the Sohotel or The Chelsea Star hotel. Has anyone stayed in either of these? I was fairly convinced about the Sohotel until I read reviews on Trip Advisor saying that there were mice and it was really noisy!

Nothing and I do mean nothing will touch priceline.com for hotel prices. Go to biddingfortravel.com for advice first. Anyone who says otherwise is wrong, flat assed, totally wrong. I've stayed at the Hilton on 50th for $109/night, the Millenium for less, and a lot of others for less.
FWIW I was born in NY and stay there about 20 nights a year for work. I often stay in or around Times Square. It is NOT the most boring part of the city, but for present day New Yorkers hating the place and revering its seedy past seems to be a religious thing, we wouldn't understand. It IS crowded with tourists. Of course thats not so in the rest of the touristed areas of the city. Right. Wanna buy a bridge? It too is FULL of tourists, but since one end is in Brooklyn, its ok to revere it. And there aren't ever tourists 8 blocks away in Central Park.....
OP, check out priceline. There are several options for staying in TS or the theater district if you want to. But to be as fair as I can be, I have to tell you that some of these folks are at least half right; the rest of the town is worth staying in, just as easy to get around from because of the subways, and interesting for different reasons.
Ed

Are you open for home exchange - ? Stay in a nice NYC-apartment while the owner stays at yours! Everything for free!! Good luck:)