There are a lot of hotels on Sunset in W.H., but as someone who lives on the B.H./W.H. border about a 10 minute walk from some of those hotels, the biggest problem is that you will be a good 15 -20 minute drive on city streets from any freeway entrance (405, 10 or 101) and the only school you’d be close to is UCLA right off the 405. It’s a great location if you want to be close to some sight sightseeing, but assuming this is to hit all of those locations on a short trip where you’ll just be sleeping in a hotel and won’t be doing sightseeing, your most central location to all the places you need to go might be an LAX hotel. They are also usually less expensive (as LA prices go).
From LAX, you’ll be almost right next to LMU and still just about 15/20 minutes up the 405 from UCLA. From UCLA, Cal Arts is another 30 miles north on the 405.
USC is near downtown about 15 miles from UCLA, which is about the same distance it is from LAX, and it can take 45 minutes or so to get there from either location because of traffic.
You might think of staying one night out in the Pasadena area where you’ll be near Occidental, USC is about 10 to 12 miles south of Occidental, and Pomona is probably about an hour East from either. From there you can loop back to LAX which is about 50 miles from Pomona.
Just some ideas. Good luck and have a safe trip!