Yes, don't miss the Beatles Story museum, especially if you love the band's early days before Brian Epstein moved their management to London. It's right next to where the Magical Mystery Tour bus departs (bus end point is right near Cavern Club and Hard Day's Night Hotel). The TI is right there too; handy place to buy postcards and get stamps to mail them. Your bus ticket gets you free entry to the Cavern Club.
If you're traveling by car, there's a large parking garage near the Albert Dock, but we parked outside the World Museum, which is an easier navigation from the Edge Lane (A5080) and closer to where the bus ends. You can pay by phone, and even top up your parking by phone if time runs out before you're ready to drive onward. Coming from the Edge Lane, whether you park at the World Museum or go on to the parking garage, watch out NOT to enter the Queensway Tunnel under the Mersey to the Wirral peninsula. (Of course, if you're coming from Wirral/Wales then this works in your favor.)
The Beatles Story could take half a day if you really want to savor every detail. I'm not sure if they sell tickets online in advance, but if so it might be worthwhile because the entry desk is small and can get backed up when a tour group arrives.
The Hard Day's Night Hotel lobby area is really wonderful to walk through as the walls are covered with photographs and the p.a. system plays Beatles music all the time. If you're hungry (note the Cavern Club serves only drinks, no food), the hotel bar area has an "Any Time At All" menu so you can sit down and have a cup of tea & scone or a sandwich; doesn't have to be a full meal.
Enjoy!