Switching cities is a lot of fun, and keeps every day interesting (it's what I'm doing too, a couple months at a time). Doing it in Asia is definitely viable, I've spent about $2k in the last 6 months hopping month-long airbnb rentals and crashing at friends'/family's with my backpack. A refreshing change after leaving the Bay Area.
India is actually a lot of fun to travel through. If you have company, getting on a train starting somewhere in the south and working your way up north visiting the major metropolises, tourist sites (and coworking spaces I guess) can be really fresh and enlightening. I strongly recommend that, if you're ok being without internet and power supplies for extended periods of time.
[see The Darjeeling Express if you haven't]
I have not spent any meaningful amount of time at Indian coworking spaces. Due to poor navigability of public transit and not having my own ride, I didn't have a good option. And heaven forbid actually having to drive on Indian roads without lots of slow practice.
Corporate internet connections tend to be a lot better (and cost a buttload), so not all "businesses" bother to get them. I have heard that coworking spaces in any of the true IT-powered metropolises -- Bangalore, Hyderabad, Mumbai, Chennai -- are much more likely to have solid internet connections, although there are coworking spaces in some of the smaller cities too (like those in Kerala).
I worked out of Microsoft's offices in Hyderabad once because a friend is there, and funnily enough they were having massive bandwidth and ping issues that day, I couldn't stream SD video without buffering pauses for my app. Maybe it was just their guest network, but I doubt it. So who knows? If people here think American ISPs are bad, you don't want to go near India...