In Bangkok I stayed at the Wild Orchid. (mind you this was in 2003) It was reasonably priced and very clean. It is in easy walking distance to Khao San Road and the Chao Phria River.
Here is an excerpt from 2003 from the site noted below:

“Wild Orchid (02-6294378*)
[RbeforeE] stayed here with us and really liked it. They have a nice open-air restaurant and internet cafe right downstairs, and a range of rooms.
Room with fan $4.75/$8 single/double.
Room with A/C, private bath, and unreliable hot water: window $13/$14 single/double, balcony $15.50.
There is one suite for $22.
*They do not take reservations.”

Don’t miss the Floating Market, whatever you do!

Check out pranatech dot com, under web dev, portfolio, wedding for tips about traveling in Thailand. There is some fantastic information in there.

In Phuket- the Best Western is nice, Bangkok anything on Kukumvit Rd. is nice and affordable.

Go to the night market to shop in Bangkok, barter, barter, barter and have fun!

Here’s where I stayed in Chiang Mai

http://www.dusit.com/hotels/thailand/chiang_mai/royal_princess/index.html

It was great- inexpensive, awesome location, very nice inside, great restaurant, great staff. The concierge in the lobby has planned sight seeing trips you can sign up for and they pick you up right at the hotel. It is very convenient. To get to great shopping just walk outside the hotel and every night is a big shopping bazaar. We loved it.

This is my favorite in Chiang Mai: 2nd Home Guest House. No frills (although right before I left, hot water became available in the shared bathroom), super cheap (well under $10 when I was there), very clean, great location (inside the moat area), and so friendly! A real family atmosphere with Dano, the owner, and her two young sons.
Here’s the address: No. 2, Rajchapakinai Rd. If you’re looking at a map of the city center, it’s right near the south gate, a block or two from the daytime food market. Look for a big green gate, or ask around.