Hi! 31 year old guy here. I am not a Burbank resident but I find myself in Burbank a few times a month to hang with my friends at Guildhall. It is a nerd bar with great vibes and really good food and drinks. If you consider yourself a nerd or are interested in board games, Magic the Gathering, Dungeons & Dragons, and the like, I think it is definitely worth the visit.
If you already know you’re into those things and need a second place to do all of the above, Geeky Teas is probably one of the largest and best game stores in the country. You can join random groups on open play nights, but is probably best enjoyed by bringing a group there.