I've flown out of Seletar with the Republic of Singapore Flying Club on a number of occasions recently (usually as a handling P2 to a Singapore PPL) and its well worth making a call to them, they're very friendly and enthusiastic.
You probably need to be in touch with them at least 24 hours ahead as they'll need your ID details to get you airside. There usually some faffing about to deliver your passport to the terminal area on the opposite side of the airfield in exchange for an airside pass, but its not too onerous.
If you can take a day out of your schedule, see if there are any seats going begging on a "cross country" (across water actually) to the Malaysian island of Pulau Tioman. Its the original setting of Bali Hai in the old movie South Pacific and fully lives up to the billing, not to mention an interesting approach to the sole runway on the island!
Even if you don't get the time to fly, its a nice place to drop by and enjoy a steak supper and soak up the club atmosphere. Not to mention the Tiger beer!