I completely feel you entirely. Walking through all those markets and shopping areas alone. Funny how seeing people together can make you feel even more isolated. I was in Argentina when they won the World Cup. Happy for them, but it was probably the lowest point for me. Literally seeing an entire country in celebration just reminded me how alone I was.
Nothing beats those school time friendships. It's nice that wherever you go, you can almost always come back to them.
Maybe staying with family will help recharge your batteries. But stay as long as you need. Taiwan (or the rest of the world) isn't going anywhere. It'll be there should you choose to return and try again.
Hard to suppress that adventurous spirit for too long.