I think Singapore is quite a safe place. Maybe this is why your guidebook is not helping u out much, by listing dangers and dangerous districts. There are none to worry much about.
What about staying in the YMCA hostel
[ Edit: Edited on Jan 23, 2007, at 2:48 AM by Mel. ]
Think that Hotel 81 is a good idea, especially those in town (Chinatown, bencoolen etc)
If u r staying longer, u may ask for long stay rates
As for hostels, think those in little india are okay but the difference is not that substantial and the comfort level may not justify the difference
It all depends on what u r looking for.... Little India is perhaps the most funplace for cultural activities.... Chinatown is a bit sterile but getting "wild"..... Orchard Road is for shoppers without a budget..... Geylang is for the adventurous (some call it the unofficial IR in Singapore).... but for a feel of how Singaporeans live, go to the HDB centers of Toa Payoh, Tampines, Jurong etc....
Is it safe in Singapore? Well.... there is some crime but nothing to write home about.... Just do as the others have suggested.... stay off the dark alleys (even these are a bit difficult to find) and stay on the main roads....