There are dozens, depending on what level of comfort you need.
One that looks really good and old-school cheap to me is Ginny Place. It is in a great location inside the moat. You can read about it here: http://www.travelfish.org/board/post/thailandadditions/7991_ginny-place-guesthouse-in-chiang-mai
Another favorite is CM Blue. You'll find details at: http://www.travelfish.org/accommodation_profile/thailand/northern_thailand/chiang_mai/chiang_mai/all/1822
Are you looking to stay at the same place for the entire month or to move around to explore different parts of the city? Cheers.
A traveler favorite is A Little Bird Guesthouse in the old city. It's one of the cheapest at 100 baht for a dorm bed and full of many like-minded wanderers.
If that doesn't suit you or your style, your best bet is just to show up and shop around before you buy or book online. There's hundreds of little guesthouses all over the old city, many that aren't on any websites so just walk around an area (I'd recommend Moon Mueang area just for the density of accomm) and pick one. There are many cheap places, say under 400 baht, so not to worry about not booking ahead and not having a place at a good price.
#3 whardy has been a member since 14/11/2011. Posts: 66
Thank you for your recommendations. I'm taking a TEFL class near chiang mai university and, unfortunately, most of the places I've found online or were recommended are about an hour walk away. I think I'm going to have to arrive a day or two early and look around.
Thanks again for your help!
#4 heavanse has been a member since 2/3/2010. Posts: 11
Your best bet is to rent a motorbike, that'll open your world up. I'm not sure of much over in that area, but if you look hard you'll find it. If you have to commute, it may be a pain, but only 20-30 baht one way (around $1 USD).
#5 whardy has been a member since 14/11/2011. Posts: 66