Personally, I think bathrooms are the very place to change a child. I try to avoid the carpet, though, as I once had an incident where a newborn peed during the diaper change and it got on the bathroom carpet (when I was a guest! eek!). I'll just put the changing pad on the floor itself. Yes, it's a bit hard. But it's only for two minutes. I can't see it being that much of an issue even for a newborn. (This reminds me that my changing pad isn't in my diaper bag at the moment--need to find it, as I keep having to use a clean diaper or one of the plastic bags as my "changing pad" when I'm out).
I would feel hugely uncomfortable changing a diaper on a bed and would probably move to the floor as soon as the host left. For one thing, my changing pad gets used on bathroom floors, so I'd be transferring germs and stuff to the bed. For another, the slight risk of leaks would lead to a *huge* problem. Give me a tile/linoleum/hardwood floor any day over something fabric/carpet.
I generally just take diapers home with me, because it's what I often have to do when out and about anyway. I have a pocket in my diaper bag that I usually put them in, so when I finish changing the diaper, I just put it in there by habit. This is after putting it in a plastic bag, especially if it's a dirty one. My MIL was really surprised when I finished changing a diaper the other day at her house and just by habit went to take it home with me, but I'd already had it packed up to go, so it wasn't much trouble. I'd be a little more loose with a diaper that was just wet, though, possibly just wrapping it up and leaving it in a trashcan. Even wet diapers can cause a stink if left out for a long time, though. Just smell the inside of a diaper pail someday. Ammonia, ick.