How much to travel?

I've been saving up for months now, every single penny I have. I truly want to leave the US and finally travel the world. I have my eye on China, and I wish to stay abroad for as long as I financially can. I was able to save up about $17,000 and can possibly come up with a few thousand more. I can do one of two things: backpack and stay at hostels, moving around until I run out of money, or I can 'homestead' by renting a monthly studio and branching out from my base of operations. Backpacking will be cheaper and more freeing but will be riskier, while 'homesteading' will cost more but will be more stable. It'll just be me. I am a 33 year old female with no children or ties keeping me in the States. I don't plan to purchase unnecessary things like trinkets or clothes, only lodging, travel, food, and experiences. I honestly have no idea how long I can stay abroad for $17-$20,000 but I truly want to be gone for as long as I can. Also, if it turns out I don't really vibe with China I can always go somewhere else. How long can this money last realistically?