So I've played for about 16 hours (ps3) and I've done only five quests. I've been exploring the map and I've come across a few vaults. Should I go in them? What will I find in there? Should I know anything about them?

I know at least one vault has a quest you might want to wait for. Vault 22. Get that quest, then go. I don't know about any others.

Quest is obtained at Camp McCarren. Or whatever the name is.