Overall, great place to rest and still be somewhat near the action! We stayed at both Srikum House (2 days turned into 5 days) and Nonni's Guest House (2 days) in February/March 2015 and they were both good.
Our room at Srikum House was clean with nice wood floors, A/C, fan, and private bathroom. It was spacious with a double bed, table, and chairs. Bed was somewhat firm cushy with the feeling of spring coils. We asked for some sheets to put as cushioning for the hip and back and the owner was accommodating. Hot water was ready within 10-15 minutes with the switch turned on and the shower knob turned about halfway. The owner was nice and we always got our needs conveyed and met.
Based in a more quiet residential area with more of a local feeling (vs touristy inside the old city), it is about a 15-minute walk from the Chiang Mai south gate, the Saturday walking market, and Night Bazaar. Plenty of street food, restaurants, massage places, convenience stores, and temples along the way. Complimentary breakfast was nice with self-serve bread, butter, jam, and coffee.
When finding your way there for the first time, the (Chiang Mai) College of Dramatic Arts might be a good landmark. Great simple, clean budget place for a budget price (~$15 USD)! We would stay here again!