Which is the cheapest hotel in Bangkok closest to the Patpong night market?

Baiyoke Boutique, First House, Grand Watergate or White Orchid?

Why the Patpong area? If you choose the First House you can shop in the Phetchaburi Road area. On Phetchaburi Road you will find lots of street vendors, malls, Panthip Computer/Electronics Plaza and a mini garment area around the soi leading up to the Baiyoke Tower Hotel.

http://www.asiarooms.com/thailand/bangkok/first_house.html?gclid=CKPSgNv8mZUCFQOIFQodGGzngQ
http://www.asiarooms.com/thailand/bangkok/first_house-hotel-location.html

From this First House location you can walk to the Skytrain stop and use that overhead rail service to take you to the Patpong area, MBK, Chatachak Weekend Market, Sukhumvit Road for more street vendors and malls and to many other places.

Good luck.

None of those hotels are too close to Patpong which is off of Silom Rd., the first three you mention are in the Pratunam area about 2 or 3 miles from Patpong, the White Orchid is in Chinatown which is further from Patpong. It would probably be easiest to take a taxi from Pratunam to Patpong or walk to the Skytrain which is not too far from the Pratunam hotels. Btw, if you're going to Patpong for the night market, most everything that is available there is available at the street stalls along Petchburi Rd. and Ratchaprarop Rd. at better prices and is also open during the day (except Mon.). If you're going for the entertainment, you might want to check hotels in the Silom Rd. area of which many are within walking distance. You can check on this website for hotels around Silom, the Sathorn area is also very close to Patpong.
http://www.hoteltravel.com/thailand/bangkok/hotels.html

None are close, but you can search by location and get a good price here:

http://www.hotelscombined.com?a_aid=781bc64c

There are plenty of cheap places to stay near Patpong.

Wall street inn http://www.discovery-thailand.com/Hotels%20Map%20Pages/Silom%20Sathorn%20Hotels%20Map.html
is cheap, and close to the Patpong night market!!

Silom City Inn is very close to Patpong, spotlessly clean, enormous rooms, great breakfats and VERY cheap.