The closest and most reasonably priced accommodation to the shala is at the Kaveri Lodge. However, depending on your budget and comfort, you are welcome to look for other options in and around Jagmohan palace in Mysore. The shala also may have some accommodation available but that is generally reserved for those who are taking their yoga classes too. Write to This email address is being protected from spambots. You need JavaScript enabled to view it. for more details.
There are plenty of eating options all around to suit every budget. Modern departmental stores with western foods and fresh Indian vegetables are easy to find.