You can check nearby HP University Shimla. I stayed there 3 years ago and the owner of the house also provided Dinner. I don't remember exactly the name. Though it was little away from Mall road but it was very nice experience. You can also ask there on arrival.
If you are talking about the main Shimla City then it is little tough to find any home stay because as you know this place is very popular tourist spot and a great place to earn profit by providing accommodation .
so if you searching for the he stays you can go to "Summerhill" which is university area and you will find many students around this area and feel free to talk to thwn and you can easily find the place to stay..