updated: 3 or 4 days Singapore itinerary, a suggestion/guide

When you arrive in Singapore, pick up a map at a tourist information booth and find out if there are discounts offered for some restaurants and places of interest. Click and check the offers at Singapore Visitors Guide. If you have 3 or more companions and have many luggages, you may go to the transportation desk where you can hire a taxi van called Maxicab or MPV by SMRT (costs higher than regular taxi). Regular taxi costs about S$15-S$20 to the city. Or, you may want to take the train or bus. The train and the bus are the cheapest and most efficient mode of transportation in Singapore (less than S$2 to the city). Directions to the train or bus are easy to follow.

The most convenient and economical option is to buy a Singapore Tourist Pass at the Changi Airport MRT station. It is a 1 to 3 day unlimited bus/train pass that you can use to travel around Singapore. Click/visit the link The Singapore Tourist Pass to get more info, buy online and check outlets where you can buy.
Tip : check all your destinations via http://www.streetdirectory.com/. You may call taxi anytime from anywhere. Phone numbers are 6555-8888 or 6552-2222 or 6552-1111. Most, if not all, websites of all the places of attractions I am referring to has rates, promotions and an instruction on how to get there (look for the GETTING HERE menu).

Suggested 4-day itinerary:

Day 1 - Sentosa Island Resort, http://www.sentosa.com.sg/, you may check the website for events, promotions/discounts and schedules here. To get to Sentosa take a train (MRT) East West (green) line going to Harbourfront. If you were not able to buy Singapore Tourist Pass, you may purchase a card through machine or ticket counter. Once you have reached Harbourfront, you may refund S$1 at the ticket machine before you go out of the station. Take Vivo City exit and go the Sentosa counter at the top floor where you can avail promotional package which I will mention below. You will ride a train called Sentosa Express from Vivo City (http://www.vivocity.com.sg/). The cost of a return train ticket is S$3 valid for the whole day.

Packaged fun attractions can be bought here or through Sentosa Express ticket counter at Vivo City Shopping Mall.

Sentosa Express:

The Sentosa Express links HarbourFront, VivoCity and St. James Power Station to Sentosa in less than four minutes.

Operating hours:

First train - 8am
Last train - 10pm
Beach Station:

First train - 8.15am
Last train - 10pm

Ticket: S$3 per person (Adult and Child aged 3 and above)

Another way of getting to Sentosa is through Sentosa Boardwalk from VivoCity Shopping Mall waterfront promenade which ends at the Sentosa Visitor Centre. Entrance fee is $1.
You may also get to Sentosa through Sentosa Rider for $5 one way or $8 full day pass when you stay at Orchard area or Marina Bay area. Buy it here.
Shuttle bus is free when you are already inside Sentosa which will go around the island and to various attractions.
You will probably spend the whole day at Sentosa because there are about 30 games/shows/attractions including the laser show at about 7 pm. This includes the underwater world and dolphin show, cinemania, the merlion, etc. You may get Sentosa map with event schedule for free at the Sentosa visitors arrival center or when you buy a ticket at the Sentosa Express, VivoCity.

Day 2 - Escape theme park and Wild Wild Wet are in the same area at Pasir Ris, http://www.wildwildwet.com/, http://www.escapethemepark.com.sg/. You may reach the place by train via East West (EW) line going to Pasir Ris station. When you leave Pasir Ris station, you may walk to get there, pls check the map at the website of escape theme park.
In the afternoon you may go to Clark Quay where the Gmax Reverse Bungy is. You may call taxi or you may take the EW line train going to Joo Koon, get off at Outram station, change train, Northeast (NE) line, get off at Clarke Quay. From there you can walk to Gmax. Pls check the website at Gmax - Xtreme Swing, for more information.

At night, you can leave for the Night Safari. The website is: http://www.nightsafari.com.sg/, check if there's a promo available.

Or you may want to go to Suntec City Shopping Centre. There, you can find the world's largest fountain. There's a laser show at about 7 or 8 pm pls check website http://www.sunteccity.com.sg/ or you may want to ride Duck/Hippo Tours at Suntec (http://www.ducktours.com.sg/) from Suntec City you may walk to Esplanade, http://www.esplanade.com/, or ride Singapore Flyer from there you may go to Mustafa Centre , http://www.mustafa.com.sg/ or to Bugis Junction for shopping.

Day 3 - Singapore Science Centre (http://www.science.edu.sg/) or Snow City, (http://www.snowcity.com.sg/). They are on the same area. Pls check the website for other promotions. After that, you may go to Suntec again or Sim Lim Square (http://www.simlimsquare.com.sg/), the electronics and gadgets shopping mall of Singapore at 1 Rochor Road or Funan DigitaLife Mall (http://www.funan.com.sg/). Funan is accessible and short walking distance from City Hall MRT station. Everyone or any taxi knows where they are. Or you may want to go to Chinatown, (http://www.chinatown.org.sg/), best time to go there is from 5 pm onwards.

Day 4 - Universal Studio Singapore is also located in Sentosa Island, to go there from VivoCity take Sentosa Express and get off at the first stop. Other ways of getting to Sentosa, please refer to Day 1.

Universal Studio 1 Day pass costs S$66/adult and $48/child.

If you have more time, visit Jurong Bird Park. Entrance fee costs S$18/adult, $12/child. Extra $5 and $3 respectively, if you prefer to ride inside the park.