UCLA and LMU are close(ish) to each other and on the west side, convenient to LAX. Cal Arts is in that same orbit though it’s up the 405 an hour or so. USC and Occidental are closer to downtown, very different dynamic. Chapman is in Orange County which is a good hour+ south, in the other direction from downtown. For all but Chapman, the most central place to use as a hub would be to stay in Hollywood or West Hollywood. There are plenty of hotels along Sunset Boulevard in West Hollywood, in all price ranges. For Chapman you may want to move to Orange County for a day or two, check out UC Irvine and return home from SNA (Orange County Airport).