Will you have a car?
BadPinktink is correct that Venice (and Santa Monica, which borders Venice to the North) are a relatively good distance away from Universal. Because much of it is "overland" driving through city streets, it's Google estimates its an hour drive to Venice Beach from Universal. We have a saying in L.A., "it can take 20 minutes or 2 hours, depending on traffic." I've met people who lived in Santa Monica for decades and never once went to Hollywood or Downtown L.A. despite it only being a distance of roughly 15-20 miles. However, you come very close to Venice on the way from Universal City to LAX airport. South of Venice is Marina Del Rey, Playa Del Rey and then LAX/Westchester. If you plan accordingly you can spend time at Venice then proceed to the airport.
BadPinktink is NOT (necessarily) correct that Universal is an hour from Hollywood, Universal City is the next stop up "the 101" (Hollywood Freeway), on the other wide of the Hollywood Hills, maybe 10 minutes from "downtown" Hollywood (caveat: not accounting for traffic, which could make it an hour...or more). This is where the San Fernando Valley starts.
The Hollywood sign can be seen from much of the city south of the Hollywood Hills (most of the city is a flat basin, so the sign lords over a lot of it), you'll most certainly see if it driving or riding to Venice. If you want a better look, there are several good views closer to the hills. You probably can't travel to Universal without spotting it as well. It's possible, and legal, but a hassle to hike to the sign, the locals don't like it since you have to cut through their neighborhoods. The restrictions are always changing.
As to the actual question of hotel, the Hilton and Sheraton are the most popular hotels in the Universal Studios Hollywood area.