The place pictured here is now closed, though I believe the outlet at the top floor of Chiang Mai Pantip Plaza is still there. (Though who knows for how much longer.. :) )
It may seem unfair to now have 3 eviews of Mexican(ish) food and still zero Italian food, even though there are lots more Italian restaurants around Chiang Mai, many of them really excellent by any standard! Perhaps it's because Mexican is so hard to find in Chiang Mai. Or just because all of the places I mentioned are relatively inexpensive little places, my favorite kind.
Burrito House fits in nicely, it's a bit out of the tourist center and quite inexpensive. Don't expect great Mexican cuisine, think 'Taco Bell' and you will definitely not be disappointed.. Perhaps even pleasantly surprised.
The place does some Italian food as well, some standard pasta dishes and pizza. And some standard fast food like fries and burgers. There's also many ice cream deserts on the colorful menu, which actually looks like a menu from some big fast food franchise! Yet the prices are very friendly indeed. I include a picture.
Burrito House has two locations in Chiang Mai, one near the Novotel / Rim Ping Supermarket on Chotana Road and this one in a soi off Suthep Road near the back entrance to Chiang Mai University. To get there continue towards CMU on Suthep road past the intersection with the Canal Road. It's then in a soi on the left, before you get to Soi Wat Umong. There's a sign on the main road.