I actually spend quite a bit of time in NYC. I average about once a month. I usally just drive in for the day, but if I am spending the night, I stay in New Jersey. Most hotels in Manhatten require a 2 night minimum to book and the lowest price I have found is between $300-$400.
After staying in some pretty pricey hotels and some pretty scary hotels, the best one I have found is the Hampton Inn in North Bergen New Jersey. It's about $100 a night and it is exactly 7 miles from Times Square Church. It is right across the George Washington Bridge. The Hotel is very nice and clean. It has a swimming pool and a nice breakfast, but it's right off the highway and there is absolutely nothing around. I would recommend renting a car in New Jersey then driving over. The parking is free at the Hotel and if you are going to Times Squre Church for the day your parking is just $2.00. Just remember to get your ticket validated at church before you leave. But there is also a commuter rail that goes over to Times Squre, but I'm not sure about Sunday. If you called the hotel they could help you out with that.
Ray's pizza is right around the corner from Times Squre Church and it's the perfect stop for lunch between service. It's a great stop for a good New York pizza and the price is low.
If you want to go shopping, but not break the bank than Cannal Street is the best. Cannal St is right in the middle of China town. It's a big outdoor market place. You take the R train right from Times Square...it cost $2.00 each way. Little Italy is right next door to China town. And Ground Zero is about 5 blocks away or a 2 minute metro ride from Little Italy.
The Zoo at central park is only about $6 a ticket and that is not far from Times Squre either. The American Natural History Musem is huge and if you happen to get a rainy day, you could easily spend 4 or 5 hours in there.
The only reason I go to NYC is Times Squre Church, but I have found alot of fun things to do while I'm there that don't cost alot of money.
I know you will be blessed by Times Squre Church, but I hope you have fun and hope all this info was helpful.
God Bless,
Tina