I'm pretty evenly balanced between introversion and extraversion, from the perspective of energy levels and recharging time. And, of course, different people are differently energizing or draining for me. But this winds up with me needing some things on the introversion side, and others on the extraversion side, and I'm very curious to hear others' ideas or approaches on these fronts!
When I'm an introvert staying with extraverts:
Assuming I have my own room, I go to "bed" earlier than I need to for sleeping purposes, escaping to my room for some quiet time before going to sleep. Similarly, I don't get up immediately after waking up. I might also/instead, take "naps", which might just be time to myself away from the action. I also often go for a little walk alone -- especially pleasant in an interesting neighborhood.
If I don't have your own room, all of this is harder. I can use my laptop or a book as a virtual shield against the world sometimes, even if there's a lot happening around me. Assuming my hosts are good enough friends for me to say, "Hey, I just need a few minutes to myself," this is usually pretty manageable.
When I'm an extravert staying with introverts:
When possible, I find out how much social time with me my hosts want. If I want more social time than that, I'll look elsewhere for that -- do I have other friends in the area? are there meetups happening for any of my online communities? is there a good club or bar for me to check out?
I also really try to make it explicit that I'm not expecting my hosts to "entertain" me (unless I am, in which case, we've probably had some direct conversations about the whole situation anyway) and invite them to let me know if they need more space from me, or to feel free to escape to their own rooms if they need down time, rather than feel obligated to be "on" in host-mode the whole time I'm there.
How do you handle introversion and extraversion as a guest?