I have walked by this place every now and then. Never stopped in, massage places not my thing, especially expensive ones.
Annie's Soapy Massage. I would call first to see if they are open.
http://www.anniesbangkok.com/
You should have scheduled a longer stay in Bangkok, especially if you are only flying to a another area in Thailand.
There is a left luggage area at the airport. Rail link to Makkasan is 15 baht now and meter taxi to this place is around 70 baht using meter only. Skytrain from Phaya Thai to Nana Skytrain stop is doable too. (The last stop on the Rail Link connects with Skytrain at Phaya Thai.) Walk to Soi 4 from the Nana Skytrain and go up Soi 4 until you see the Nana Entertainment Plaza, almost across the street is a hotel parking area this place is on that connecting soi between Soi 4 and Soi 2.
Good luck.