What do you miss out on if not staying in the official hotel for PyCon (or other tech conferences)?
Not a lot really, provided you’re within walking distance of the venue. The official conference hotel for an event like PyCon will likely have a hallway track that continues until the early hours (people hanging out and hacking on things in the hotel lobby) but staying in a different place won’t prevent you from joining in with that.
Walking distance IS important if you plan to drink with people in the hotel bar.
I suppose one thing you might miss out on is having breakfast with other attendees—but chances are the conference provides breakfast so that won’t be an issue either.
It can be nice to be able to pop back to your room for five minutes during the day—to charge things, deal with a problem that comes up or just have a few minutes to yourself.
I did once stay in a hotel that wasn’t walking distance from the main venue and it sucked: I missed out on lots of impromptu evening stuff because I had to consider the logistics of getting back again.