I'm currently living in Chiang Mai, Thailand, where I share a house with a friend (I have my own bedroom) for $70/month. I eat out for every meal, even though it's generally at cheaper Thai restaurants. I have plenty of money to go out drinking with friends and to train at a kickboxing gym. I can do all this easily for under $700/month. There are lots of cafes with free wifi, and I get wifi in my house. The weather is temperate/hot year round. Chiang Mai is a great place to live, but you could live pretty much anywhere in Thailand with similar expenses.

Vietnam and Indonesia can be done even cheaper, and their internet connections are just as plentiful, at least in cities. However, it's easier to get longer-term tourist visas for Thailand.