I saw a lot of people have mentioned Bangalore, India.

I would like to suggest Prague, Czech Republic. The cost of living is low compared to rest of the western European cities. With $1000, you can live quite comfortably. You can get a decent 1bhk or a studio apartment with $400 or less. This also includes expenses on utilities such as internet, heating, electricity etc. The internet connection is very fast. I pay around $30/month for a 100Mbps connection(In a dorm). Apart from that, food, transportation and leisure activities won't cost you more than $200.

As far as the city is concerned, it is one of most beautiful cities in the world. Prague has one of the best public transportation systems in Europe. There are a lot of tourist places and because of its geographical location, you can easily travel to any part of the Europe within a couple of hours very cheaply. The winters can be a bit cold but it doesn't snow that heavily. I have lived here only for a couple of months, so I haven't seen a Prague summer. But I have heard that the summers can be hot. But you can cool off with a traditional Czech beer in just $1.5.

Good luck with your decision.