Suggestions for 2 month long stay in Mysore

I've been on a 'workation' for the last 4 months or so, first in South Goa and then in Pondicherry / Auroville. Am planning to spend a couple of months in Mysore next and would like to get some recommendations on areas in which to look for a room / apartment. I've been looking on AirBnB for a place, but the listings there describe the property itself more and not so much the neighbourhood or surrounding area. So if I can get a sense of where to look, then I can close in on a particular option or two. Basically, I just want to be in a quiet place with a lot of nature to walk around in for an hour in the morning and an hour in the evening. I work about 5 hours or so and go out in the morning and evening to walk in nature. I practice barefoot walking as a meditation practice, but it need not be barefoot necessarily. Large park/ forest / field / hill / lake etc. would be nice. Preferably not a lot of buildings and cars. Don't mind being far from the city or outside it in the countryside as long as I can get a stable broadband connection. Not much inclined to the usual visitors / tourists things like visiting Mysore palace or museum or temples or trying out local food, etcetera. Thanks.