Although Singapore is expensive, you can still travel around it on a shoe string.
There are budget hotels in Singapore that are pretty affordable. If you want somewhere even cheaper to stay, consider a hostel in Singapore targeting at Singapore backpackers.
There are several hostels in Singapore, located mainly in the city area. Among them are Bencoolen, Little India and Chinatown. The prices a night can be as low as $15.
While the hotels are inexpensive, they are clean and comfortable.
Many of these hostels even provide free breakfast.
As the number of hostels are limited, the more popular ones are usually fully booked. As a rule of thumb, book your room one month before checking in.