I guess it partly depends on what you define as interesting! The first thing that came to mind was a journey from Bidston to Shotton, which will (hopefully soon) be in the hands of either 230s or 197s in the foreseeable future. So a chance to have a ride on a 150 along the line before it's all change. There's of course then Hawarden Bridge, which I recall is worth a look at. I haven't been up the line for a very long time myself, it was still all single 153s when I last did it.
There's then the unusual triangular station at Earlestown, which memory tells me is the only triangular station apart from Shipley. There's also the TfW services via the Halton Curve, which I've seen all sorts on whenever I've been up there on previous visits. I've seen 150s, pairs of 153s, 158s and even a 175 on that route before, so worth a look if Sprinters are your thing
Of course you also have the Merseyrail 507s and 508s, they've got to be worth a ride before the 777s eventually enter service! Maybe a spin on one out to West Kirby for a bit of a walkabout and so on before returning to Liverpool? I would recommend getting a gelato from the place pretty close to the station, but it may be a bit too chilly for that

New Brighton has a bit more going on near its station, it could be a nice seafront walkabout there before picking up a hot beverage and so on before the journey back? Pro Tip, the Lavazza coffee machine in the ticket office at New Brighton does really nice coffee at a reasonable price. It may not be the biggest cup in the world, but it's also not too bad. If nothing else, you could potentially do the journey out to there, step back a train and get photos of any 507s and 508s stabled at New Brighton, as they stable trains there on the sidings immediately next to the platforms. Said journey takes you past Birkenhead depot, and you may get to see one or more of the TfW 230s on said depot.
I think there's 769s diagrammed to work on Saturdays, something a bit different or at the very least interesting. I don't think 319s operate much on the line through Bolton (maybe not at all?) but that was certainly always good fun in the motor coach

Depending on what service you take over the Chat Moss route, you might get a 323 and they remain one of my all-time favourite EMUs, so I'm biased but I'd class that as interesting.
Like I say, it depends on what you call interesting!