When I had a smart phone, the methods of communicating with me were email, work email, work IM, facebook, skype, hangouts, phone, and text. Because of work, it wasn't possible to do airplane mode and it wasn't possible to do a sleep-mode bypass for specific phone numbers because of the oncall situations.
The only way I could find to manage notifications properly was to essentially create a black list for my contacts and blacklist all apps. It worked up until somebody on the black list needs to reach me, so they get added to the white list to avoid the issue. Oh, shit, they're texting me while I'm trying to work - back to the whitelist!
It eventually just becomes an incredibly tedious task to manage your notifications properly - which in itself is a dang distraction.
Agreed on leaving phones elsewhere - just as long as you live in a decent area. Some of the most awkward times I've had recently are while hanging out with others where everyone is on their phones and I can really only just twiddle my thumb. Bringing the subject only results in "hipster" comments, rather than an actual discussion.