I've been to Samui, Krabi, and Phuket in various Augusts and any of them are workable. Khao Lak is essentially same weather as Phuket. Samui is generally drier this time of year but it's a small island and has less to do/see in your non-beach time. Boat trips to nearby places (Ko Tao, Angthong Ntl Marine Park, etc.) run pretty reliably. Phuket and Krabi will almost certainly be cloudier and have rain, though usually it pours down only for a bit in the afternoons, not the whole day. So you can still get some decent beach time in...unless very unlucky. Be advised that the August water at the Andaman side beaches can be rough, with rips and undertows to the point of being unsafe to enter and swim. Sometimes low tide is OK if you're a decent swimmer. Swimming pool may be your friend during this time of year on Andaman side. And boat service--especially longtails and smaller craft--will often have to be curtailed due to heavy waves. Larger boat craft such as to/from Phi Phi will be more uncomfortable trip if you're seasick prone, but still running. However, Phuket and Krabi each have more in the area to see and do. Many places in Khao Lak will be shut in August, so it will be very quiet up there--maybe too much so. In August, prices will be low on the Andaman side and not so low on the Samui side.

I've also been to Pattaya in August, and I wouldn't recommend going there in August--or any other time of year. I'd rather sit in Phuket in the rain than Pattaya in the sun.

BTW, Thai flies into Ko Samui now, but from Singapore, you'd have to connect in Bangkok. If you must come from Singapore, you could also check if any flights go direct SIN to Had Yai, then train or bus up to Surat Thani and get ferry to Samui.