I don't know specifically for the Hilton, but most hotels offer Internet access through their business center. However, the charge is usually quite high. I remember once last year, while waiting for some copies to be made, someone asking at the Westin, and the charge seemed several times what you can find outside. (This was before the Westin had high speed internet access in the rooms, at a much more reasonable rate.)
I have a local access phone number in Singapore so although I'd seen a number of places offering Internet access by the hour usually in a smaller shopping center, I've never tried to remember just where they are located....
Try this number while you're in Singapore:
1900-7-777-777. CitySearchTM is an operator-assisted Yellow Pages Enquiry Service which operates daily from 7am to 11pm (Singapore time).
You could also try looking in Sim Lim or Funan; even if you don't find a place with Internet access there, one of the many shops selling computers could probably tell you where to go.
edited to add the bit about high speed internet access in the Westin rooms.
[This message has been edited by siliconengineer (edited 08-22-2001).]