OK, 8 nights is a good amount of time for LA and
Disneyland and there is plenty to do.
You have many possibilities but the main thing you need to do is when visiting Disneyland, stay near Disneyland. When visiting LA, stay in LA. You do not want to be commuting between LA and Disneyland multiple times. Also look at airports besides LAX to fly in and out of. SNA (Santa Ana John Wayve airport) is close to Disneyland. LGB (Long Beach) and BUR (Burbank) are in the LA area. I’m assuming you’ll be arriving from some other location in the USA which means these airports should be easy enough for you to use.
So I would keep pushing for 3 days at Disneyland. There are close to 100 attractions between the 2 parks as well as Knotts Berry Farm nearby. There are also great beachside towns near Anaheim, Huntington Beach, Newport Beach and Laguna Beach. You could land at SNA and visit one or 2 of these areas on your arrival day, they are about 20-30 mins from SNA and 15-40 mins from the Disneyland Resort Area (DLR) depending on traffic. Great shopping at the Outlets at Orange as well 10-15 mins from the DLR if that interests you.
For accommodation in Anameim, there are literally dozens of hotels and motels within 5-20 mins walk of the parks. The ones along S Harbor from S Manchester down to W Katella are the best located with plenty of dining options and easy access to the parks.
4n in Anaheim and 4n in LA would be a good mix.
As for LA, you could spend days hiking just in Griffith Park but there’s plenty of other places to do so. There are plenty of trails in the Santa Monica Mountains and Topanga State Park inland from Malibu and the Pacific Palisades. You can rent bikes along the coast and ride the bike paths around Santa Monica, Venice Beach or Manhattan Beach. You can walk from Lake Hollywood Park up to the Hollywood sign and there are trails and lookouts all around the Hollywood Hills, Laurel Canyon and Baldwin Hills Scenic Overlook.
you may not like Museums but how about seeing a real Space Shuttle at the California Science Centre? Or the La Brea Tarpits, geological activity right in the middle of the city. Or The Getty Centre with incredible views across the city? Or the Petersen Automotive Museum with cars from the movies, famous race cars and vintage cars. You also have the Original Farmers Market, Grand Central Market, Olvera Street, Santa Monica (including the Pier), Koreatown, LA Live area, Universal Studios and plenty of shopping.
As for where to stay in LA, depends on your Budget but Beverly Hills, Beverly Grove, Hollywood, West Hollywood and Santa Monica are all good options.