If you're staying near Hollywood Blvd, then obviously there's tons to do in walking distance.
Amoeba Records World famous record store with an impressive collection of Vinyl, rare dvd's, cd's etc. They often have live music by sometimes well known acts. It's also a good pre game before you walk next door to the....
Arclight Cinerama Dome One of two remaining Cinemascope screens on the planet, and also the mechs of fancy theater going in LA. If you're here you gotta check out one movie there. There or...
The New Beverly Theater This is the theater Patton Oswalt writes about in his most recent book. It is now owned and programmed by Quentin Tarantino. Mostly revivals, 100 seats tops, and the popcorn isn't the best. But damn if it isn't the most charming theater in the city.
Meltdown Comics I'm a bit biased because I'm friends with the owner, but this is the comic book mechs of Los Angeles. I literally ran into Frank Darabont doing his weekly pull here. Also, Nerdist has their theater in the back and they do the weekly MELTDOWN COMEDY Show with Kumail Nianjani and Jonah Ray. THere's something awesome happening literally every night.
Santa Monica Pier/Venice Boardwalk I'm a beach kid, and I'd be remiss without mentioning the Golden Coast. If you want a fairly safe, slightly touristy fun time, including some carnival style hoopla, Santa Monica is the way to go. If you want a hippie explosion of street artists mixing with street basketball players and old school, territorial-as-fuck surfers under a thick cloud of weed smoke, Venice is for you. Both are equally fun.
Restaurants Near Hollywood, I would recommend Blue C Sushi, Chandara, Petit Troi, Pizzeria Mozza, Maude, Ink, and Red Medicine. If you want to drive a bit, the best Ramen on the entire west coast of this continent is Tsujita off of Sawtelle in Santa Monica. If you want the closest thing to Texas BBQ, Barrel and Ashes up in Studio City. If you want the whole of Los Angeles summed up into one place, POT in Koreatown.