You have access to
TG's Royal Silk and Royal Orchid Lounges (there are a number of them sprinkled around; while reasonably comfortable, all offer pretty similar, albeit basic, amenities) as a Star Alliance Gold member. As your onward flight isn't on
TG, I don't think you have access to the Royal Orchid Spa (which offers complimentary massage to
TG's F & C class pax). A visit to
SQ's Silver Kris Lounge wouldn't be a waste of time either as it has much better hot food and drinks than
TG's lounges, but has no showers, which
TG has.
If you need a dayroom for a couple of hours and don't want to exit the airport, there's really only Louis Tavern. It's not cheap though. A couple of hours costs the same as one night's hotel room in Bangkok.
http://www.dayrooms-ciplounges.com/
There's also the airport Novotel, which is the nearest landside hotel connected to the airport via tunnel. Rates are not cheap either. You can pre-book, but from what I'd read elsewhere, you can apparently get discounts just turning up on the day but obviously that's a risk.