The easiest method to explore Singapore would be to do exactly what the locals do. You heard right, do stuff that are 'non-touristy'. I've compiled a summary of places and things to do in Singapore that are mostly free, other than a bottle of drink and transport fares. Hope you will discover them useful and have fun!
1. Grab your 20 megapixel camera and head down to Chinatown .... ok, ok, 2 million pixel is equally as good. Try taking some pictures from the old shops and their almost 90 degrees staircases. If you want taking pictures of elderly people, there are many hanging out the wet market not doing anything.
2. Visit Bukit Timah Nature Reserve for mountain biking or walk around and smell the green. Bring a bottle of water and shades.
3. Have a ferry (cost only $2) to Pulau Ubin and explore the island. You can also rent a bike or worn-out motocycle. Try going for a taxi if you can locate one, they are able to climb rough terrains much better than jeeps. Explore some of the Malay kampungs and prawn farms.
4. Visit the Changi Prison. It's free entrance for tourist and inmates. Drop by the museum and chapel for some WW2 history and photos.
5. Visit the Siang Lim Si temple at Toa Payoh. Watch people get blessed. For the non-believers, you can count the number of deities inside ... it ought to occupy you for just one hour.
6. Visit the New england Park for any swim and then satay-bee hoon in the hawker centre.
7. Take a train to Changi Airport. Buy two glasses of coffee, look for a comfortable pillar within the departure hall viewing gallery, watch planes take off and ask yourself your reason for this is not on the plane at risk of a vacation.
8. Take a map and walk through MacRitchie Reservoir.
9. Go Sim Lim Square and check out the latest laptops and hardware.
10. Go jogging from Kallang River to Benjamin Sheares Bridge.
11. Have a train from the Tanjong Pagar Railway Station. You can go over to Malaysia and back within a day.
12. Try water skiing at Pungol.
13. Make your own kite and fly them in the Marine South open field. After that, you can have a delicious steamboat dinner at the many steamboat restaurant nearby.
14. Go to the Flea Market at Sungei Road. Many people called it the Thieves Market since most of the things that sold there aren't bought by the merchants.
15. Go cycling in the Sembawang Park. Quiet and nice even for fun on saturday. Cycle towards the end and you may see a few of the big ships refuelling.
16. Bring your own pit and barbeque along the Upper Pierce Reservoir. But when you feel oily, don't jump in to the reservoir, you may find themselves in Point no. 4.
17. Go to the Tekka Market at Serangoon Road for a number of vegetables and fruit. There is a stall selling one of the best Bryani Chicken Rice I've ever tasted.
18. Go fishing at Pasir Ris Park.
19. Go to the Kinokuniya Bookstore.If your are dizzy after browing the library size bookstore, sit down for any cup of tea at the cafe within the bookstore. If you feel like a bookworm that day, then go to the Borders bookstore for a second helping.
20. Go to the Sungei Buloh Nature Park. Bring binoculars and do bird watching. After that, you can buy some hydroponic vegetables home at the nearby farms.