What are some suggestions for short-term apartment rentals in Chiang Mai near the old city?

Hi, My husband and I are arriving in Chiang Mai on November 30. We are looking for a short term apartment for four months. We want to be near the old city, walking distance to restaurants, cafes, etc as we will not have a car. Or at least an area where we can get red trucks, tuk tuks, or grab. We are looking a for a 40+ sqm apartment with good lighting, king or queen size bed, terrace and washing machine. A pool and gym would be great. Our budget is up to 21,000 bhat, a little more if very special. Any suggestions?Thank you very much.