I’ve had 5 trips to Liverpool, hope this helps.
I wouldn’t do it as a day trip, it’s slightly over two hours on the train each way, plus the time to and from the train stations as well as waiting for the train.
The National Trust tour is excellent , that gets you inside John and Paul’s childhood homes. Very fascinating and if you’ve got someone who isn’t a fanatic, it’s a great glimpse into post World War II Britain. This isn’t Leave it to Beaver nostalgia. Booking in advance is a must
The Magical Mystery Tour is fun and good for a casual fan, there’s Beatles music playing throughout the trip and stops at Penny Lane, Strawberry Field, and George Harrison’s house. It can be booked on the day of departure, maybe a day or so in advance during peak tourist season.
The Beatles Story is a bit overpriced but fun. Halfway though the tour, sit down in the replica plane that took the Beatles to America, the audio tour fills in a lot of the gaps as the museum kinda jumps from Beatlemania to Sgt Pepper.
Mathew Street is also worth a visit, the Cavern is a replica, but it’s loads of fun.
Respond back for more ideas if you’re interested. I’m a fanatic and I had the time of my life showing a fellow American around Liverpool last trip.