The rooms at the Doubletree in Times Square are a nice size for Manhattan. Check them out online (hilton.com and tripadvisor.com). They have a king (or queen) bedroom, separate bath, and "living room" area with a sofa bed. Don't know if that will be large enough for your family, but maybe one of the kids could sleep on a cot or you could request a larger room.
If you decide to bid on one of those sites where you name your own price, be careful. We got burned on our last NYC trip. We bid on a 4 star hotel and wound up at the W on Lexington (close of AG store). The hotel was very chic, but NOT kid friendly at all. There was only one bed in the room and the room was extremely small (about 150sqft.).
We did the afternoon tea at AG and loved it! Plenty of food and the kids had a great time. Trattoria Trecolori is an excellent restaurant! Good Italian food. Our kids did fine there. The kids also enjoyed Toys R Us (with a ferris wheel inside) and the M&M store. The Museum of Natural History was a hit with them too.
Have a great trip!