Planning direct tour of Singapore and ideal itinerary !

Since it's one of the most expensive cities in the world, Singapore and "budget" do not come together easily.
Flats tend to be small and crowded, and subletting short-term rooms is not allowed (people who do it nevertheless are often less than honest!). So, unless you have some personal friends or family whom you can stay with, I recommend booking a budget hotel, which can cost as little as S$80/night for a double room (S$100 with attached bath).
City tours and outings to suburban sights (mostly by bus) are available from the Tourism Board and some companies, but most things can be easily visited on your own by public transport. Get a good guidebook!