NYC is a huge, very diverse city - and although never cheap, there are certainly areas that are far less costly than TSq, and still are nice. The Marriott in Brooklyn (for example) is often very reasonable on the weekend, and would offer a different perspective of the city.

And remember, there really isn't a huge advantage to staying in a full service property on the weekend, as the CL is not open.

Were I you I would be looking at
1) a Res Inn so I would get free breakfast, and have a fridge for snacks, drinks, light meals, etc
2) Marriott Reward specials each week (they come out on Mon -Tue)
3) learn the rules of LNF BRG and search away...I saved $185 per night last time around!

Finally, if it is just a weekend now and then? Talk to the Front Desk. To keep you full rate weekday visit, they may be willing to cut you a pretty good deal on a weekend or two. Probably not much more than occasionally, as these hotels stay full 7 days a a week - but it cannot hurt to ask.