With either of Evan's posts for good suggestions - MRT into town (reliable and do-able, last train back to airport around 11:25pm), or exploring the terminals. Paid lounges are also available, but may be better to sit in a bar or at one of the cafes/restaurants and have a meal. There's also free movies shown, plenty of expensive branded shops and the odd less expensive shop - all airside.
Landside (through immigration which takes all of 2 or 3 minutes) if she doesn't want to go into town on the MRT, at the airport there are some more shops including a typical Singaporean "food centre" in the basement of T3 for cheaper food, and lots of people occupying themselves with the national pasttime - eating!
Oh a note for boarding the Beijing flight - as with most SQ flights, the gate opens a while before the flight - but until the flight is boarding, it is basically just entering a holding pen, personally I'd rather stay in the rest of the terminal until the flight physically starts boarding (as indicated by the displays), but each to their own. Boarding usually starts quite early though, so if your wife wants to settle in to the plane for the next flight that's good and can do so early, or at the other end of the spectrum, if she want's to stay off the aircraft for as long as possible, boarding stops strictly 10mins before departure, so boarding 15mins before departure is entirely feasible without any need to panic (from about 15-20 mins out displays will indicate flight closing - but doesn't actually close until 10mins out).
