Never heard of a free night hotel offered with the layover. They do offer free tour on their own tour buses.As for the other part, there are several hotels that are nice and in the area.
Orchard (right next door to OT)
Hilton (across the street from OT)
Hyatt (Brix is in the basement)
Royal Plaza (across the street from Hyatt)
Marriott (2 doors down from Hyatt)
There are several other hotels in immediate vicinity.
UPDATE: They do offer layover hotels, but not right at the intersection. http://www.singaporeair.com/saa/en_UK/content/local/US/promotions/2_Nights_Free.jsp
Both hotels offered are near the Esplanade or Raffles city complex and you're going to cab it to either Orchard or Geylang.
(looks as though you have to originate the flight in LAX and not SFO--don't know if the cost of changing ticket and flight to LA is worth it as I'm sure you can probably get a hotel for less than the redirect costs and effort)
Although hotel prices have gone up somewhat considerably in the past two years (probably a combo of exchange rate and increase of priceline rates), you might bid a decent rate or use latestays.com
(Latestays shows the Copthorne-Orchid at $112 USD)
Bidding for Travel shows some decent prices at Marriott and the Holiday Inn-Atrium (which is not to be confused with the HI in Orchard area, but a decent spot).
If it were me, I'd bid 4* in Orchard area and see what you get or just try to book the Orchard. That said, I really like the Marriott.