I stayed there two years ago, I think there was one on site but could have moved out and my memory might be wrong. But you are near the MRT and take that over to Asoke station, and walk up towards Nana area or take the BTS over to Nana and you will find 100's of tailors. Very simple. The transport in BKK a child can figure out, fast, clean and cheap. I wouldn't look for a tailor near your hotel, I'd go out and find a tailor that you like. Won't take long, and they are open late if you work all day long.

Plus... I'd be willing to bet that you could find one close to that hotel (I just happen to go to my same tailor on Sukhumvit) as you can find a tailor in every corner in BKK even in the electronics mall called Pantip there is a decent tailor.