My favorite Times Square hotels are the Westin on 43/8 or the Hilton Garden Inn on 8th between 48/49. They can both be reasonable (reasonable meaning under $225 a night) if you book at the right time. Often it's not always about what days you want to travel, it's about what days are you looking at the prices. You gotta be careful with the cheap hotels in New York City because cheap in New York City can often mean anything from lack of cleanliness to having to share a bathroom (and no I'm not even talking about hostels).
When I am really pinched in terms of finances, I go to Mayfair Hotel on 49th and 8th. It is always a good deal cheaper than everything else, but the bed is terribly uncomfortable, there is nowhere to put your bag other than your bed, nowhere to hang clothes, and nowhere to just put down your wallet/money/etc. Seems like meaningless things but when you are out all day sometimes you just want a LITTLE comfort in your hotel room.
Stay away from Broadway Budget on W. 38th Street. The one time I stayed there, the window in my room had no window covering on it. Three different times when I came back to my room there was a woman in my room who claimed to be a maid who was sitting on my bed texting. She had no cleaning equipment. I called the front desk and they denied the woman was there. People banged on my door all night and jiggled the doorknob. At one point I threatened to call the police if they didn't get the people out of the hallway. Again the front desk denied anyone was there, but when I threatened to call police, somebody did come out and tell all the hallway people to leave. Truly creepy!
Other decent hotels are Millennium Broadway, Gallivant, Hyatt Centric, Crowne Plaza.
Watch out because a lot of these hotels are charging sneaky facilities fees which can often be $30-40 PER NIGHT! Paramount and Row are the worst offenders for that. And watch out for Row because the lobby is complete pandemonium and the front desk staff is not in the mood to deal with anybody. To check in at the Row, you have to wait in a long, often 40-45 minute line, then if you room isn't ready, you have to wait in another 30-45 minute line to have to your bags stored. And then the same thing when you want to check out. And often the elevators at the Row are so crowded you have to wait in (sorry it's New York:) ON a line to get in the elevator!