Singapore is still possible with a shoestring budget. Singapore was my first stop over night stop on my Southeast Asia journey. If you are not aware, Singapore has quit a few rules to follow in public (check the picture below).
There are more rules, just make sure to check out the laws before traveling to any country.
I stayed at Backpackers Inn Chinatown. It was cheap (hostel) by Singapore standards. It is in a great location. The hostel offers free laundry, which many hostels do not offer free laundry. They have two computers with internet for free usage. Water cooler with free refills is included, which is a wonderful way to save money. The Chinatown food market was about 5 minute walk from the hostel. The market had the best food I had in Southeast Asia and the food is cheap. The price of beer, even at shops like 7/11, is expensive. Chinatown has some decent shopping.
Many restaurants are over priced, I suggest eating market or street foods, that is, if you are trying to save money. Little India has good India food, with a few street vendors. Riverside Point should definitely be checked out, but will be pricey.
People can go to the observation deck for Sands Maria Bay Hotel but I was told only guest can go to the pool. Before I went to Singapore, I read from different sources that you could pay to get to the pool on certain days, but was told otherwise at the hotel. I spoke with a few backpackers that said they snuck up to the pool, so there is that option.
The hotel has a casino opened to the public, including shopping (shopping is everywhere in the city). There is an forest where you can walk around not too far behind the hotel.