Transport from the airport is quite easy. The 2 best ways to get from airport to your accommodation is either via the Train (very cheap less than S$1.50 per person to get to the city). Depending on which terminal you arrive you may need to take the SKYTRAIN (free) to the train terminal. Once you get there you'll need to purchase a SMRT card - this is $12.00 and includes $7 credit. Take the train to Tenah Merah (2 Stops) then make sure you exit onto the right platform to head towards JOO KOON (the west) and not PASIR RIS (the far east). Allow about 30-45minutes to arrive in the Central Business District of Singapore (Stops include Bugis, City Hall, Raffles Place)
If you decide to catch a taxi to your hotel or hostel, you can expect to pay around S$15-25 for the trip (There is a surcharge of 25% during peak hour 6am-9.30am and 6pm-12pm and 50% from midnight to 6am) - so this can be more convenient especially if you have 3 or 4 people with you. Will take about half the time, but this depends on what time you are arriving - Peak hour can get very congested and take twice as long (and more expensive) - generally best to avoid traveling around 7.30-9.30am and 4.30-7.30pm.
Accommodation in Singapore is quiet expensive for hotels. For $100 a night you'll be getting very average accommodation. But for the most budget accommodation the rates are quiet reasonable - you can expect to pay somewhere between $20-25 per night for a hostel / backpacker. Try tripadvisor for some options for temporary home stays.
For basic food, expect to be paying anywhere from $3-5 for a meal at hawker centres. Take away and casual eating places expect to spend $7-12. Check out hungrygowhere, FoodPanda, UrbanSpoon, ieatishootipost, TimeOut or Yelp for recommendations on places to eat.
There are 3 main providers for your mobile: Singtel, Starhub and M1. All three offer prepaid plans for around S$15-18 that should last you the 5 days. You'll have to allocate some of the credit for data if you wish to add internet access to your plan. Most malls will have shops from these 3 companies.
For more information about Singapore - check out the Your Singapore website.
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