Tips - 1. Travel as light as possible. You need much less than you will initially think. 2. If you have to work, then I would suggest that renting an apartment is better, hostel's etc are too noisy and transient. 3. Don't expect the internet to work anywhere you go, even if you are told that it will work ;-) Your best bet is a 4G SIM, Pocket 4G<->Wifi Router (or your mobile phone), and an unlimited data package. Or preferably, two SIMs from competing networks, as some places have much better coverage than others. 4. I tended to stay for a minimum of 4 weeks (occasionally 2) in the same place. Otherwise, the constant travelling and planning takes a lot of time out of your work days.
I primarily stay in SEA where I never spend more than $1-2k/mo depending on how luxurious my apartment is (anywhere between $300 - $1000/mo). I stayed in a studio in Thailand for $150/mo my first time there 15 min walk from the sky train so super cheap deals can be found. Most require a 3-6 month minimum lease, but if you factor in the cost savings it's sometimes worth it even if you won't be there the full 3-6 months.
Try it for a couple months and see how you like it before fully committing, not a single person I know personally that has tried it, lasted more then 6 months. And the few stories I've heard of contacts that did last, ended up destroying their business by focusing on other things too much.
Good luck, I only lasted two months and realized a home base is nice to have.
BTW, $3k/month will get you a luxurious life in a country like India or Thailand. Let me know if you are interested in couchsurfing to try it.