If you're driving, use the park and ride - there's a few, so the best one will depend on where you're coming from, but one is at the designer outlet, so you might also want to visit there. Or go on the train.
I like to walk around the walls and just wander around, past the Minster, along the river, up the Shambles etc. There's a cat trail (pictures and models of cats on buildings and in windows), but when I tried to do it, it was too busy to look for the cats and not bump into people as well.
There's a street food market with seating near the Shambles, I like to eat there.
I presume you mean your DH is going to the Railway Museum? I'm not particularly interested in trains, but I liked the Royal Train and the Japanese bullet train.
I went in Clifford's tower shortly after it reopened, it's impressive, but it seemed expensive for what it was, and I had a half price entry (M&S Sparks offer I think).