The monastery is "not open for business", as one of the monks reminded me. Normally only practitioners can stay. But I also had the goal of teaching science and computers to whoever was interested, and there are 500 children and teenagers here.
I'm sure you could find a monastery to stay in. For all the rigidity of the core monastic rules, I have found them to be remarkably flexible and pragmatic about daily life. If you're interested, email me. There are some wonderful places in the Himalayas.
I was in Northern India about 4 years ago for 2 months, and traveling (which is several times more expansive than just staying in one place, especially since I ate at restaurants and did all kinds of touristy things) cost me about 300-400 usd/month.