Lots of places in Pakistan and India you can do that on $1000 USD a month. If you don't do really well with hot weather you could pick a traditional hill station location (Murree, Darjeeling, Shimla, etc). They have lots of domestic tourism accommodation, I'm sure it wouldn't be impossible to negotiate month-to-month terms with some of the property owners there.
Between that and this recent thread on reddit: https://www.reddit.com/r/pakistan/comments/pb5l2k/how_can_yo...
I had been ranking it lower on my travel wish-list.