I've been there.
Try finding a YMCA there, they are pretty cheap, and they are just hotels, it's odd, but that's where we stayed. The rooms were decent. All you would need really. Beds, no double/queen, but you can push two together. TV. Shower. Toilet. Breakfast. Elevators. Air Con. And there is no gym or anything like that. So, I don't know what the deal is, but it's just a hotel.
Website
Rooms are S$90 = 58 USD
Oh, and take a cab or subway everywhere. Cheap and safe.
If you want to go to the beach, go to malaysa. Singapore is known for horrible beaches. (and that little resort island they have sucks bad.)
Alcohol is really expensive. $20 for a six pack. $8/beer at a bar, etc.