I realize that your stated purpose in visiting NYC is seeing shows, but Times Square is a nightmare! Hordes of tourists filling every inch of sidewalk space. If you are not bothered by this, then there’s no problem staying in TS. I find it a bit too frenetic, and I lived in NYC for years. You could easily stay w/in walking distance of theaters w/o having to stay in TS.
You might want to subscribe to Travel Zoo NY. Here is the link to the hotel ‘deals’. Most of these are only valid through early September, so you may want to check back in a couple of weeks.
http://www.travelzoo.com/hotels/new-york/
I rarely stay in hotels in NYC since I live so close, but have stayed at two that worked for small groups and were relatively inexpensive.
The Affinia properties appear to be converted apt buildings so devoid of typical lobby amenities, but offering HUGE living space, by NYC standards. Some are studio set-ups so the three of you could share one space.
http://www.affinia.com/city-overview-nyc
The other hotel where we have stayed for a ‘girls’ weekend’ is the San Carlos. Again, it offered suites so that four women could share adjoined space. It is a little more expensive, and rooms are less spacious but nicer than the Affinia properties.
http://www.sancarloshotel.com
Friends recently stayed at the Park Lane right on Central Park South. While the rooms & bathrooms need an update, they were spacious (by NYC standards) and surprisingly less expensive than I had expected. Mandatory ‘resort fee’ included free ‘Happy Hour’ that offered wine, beer, & nibbles in a huge 2nd floor room overlooking the park. Excellent vantage.
http://www.parklanenewyork.com
As @college_query suggested, the Circle Line cruise is fun. They honor AAA discounts when purchasing tickets, or they used to.
I don’t know if you are looking for other activity suggestions, but walking the High Line is fun, and free. The 9-11 Museum is now open. I drag out of town friends though Grand Central Terminal @ 42nd & Lex, the NY Public Library @ 42nd & 5th, and the old Post Office at 33rd & 8th.
You can have an inexpensive meal at Bouchon Bakery at Columbus Circle and enjoy a wonderful view of the park. If you wish to spend money to enjoy a better view from a higher vantage, there is the Mandarin Oriental, but a drink will set you back $18.
Probably more info than you wanted!