I've done this exact same thing as mileage run. (BOS-LAX last february).
My SO had never been and I had been a few times. so we rented the cheap car from FOX car rental (book on their site and book one class below what you want then print out coupon for free one class upgrade). It was < $15. Then just gave her the grand tour. Sunset, BH, Hollywierd, hollywood hills, santa monica, venice etc. A trip to In-N-out was also in the mix.