Wow, brutally short

You're right that you need something close to an airport at minimum, with Phuket and Samui qualifying. Both are heavily built up, though beaches are still nice. There's also Krabi and Ao Nang. If u want something really memorable, use the full day for a boat daytrip to either Phi Phi Don and Phi Phi Le out of Phuket or Hat Rai Leh out of Krabi. Those are the places that you see on all the postcards.

If it were me, I'd just take a taxi or bus to Hua Hin, which is the closest beach to Bangkok that's pretty nice (and isn't crazily built up like Pattaya, where the beach isn't that good anyway).