The Hope Street Hotel is good, but I don't think it has a spa.
The Hilton is very central, and quite bling.
What to see depends on what interests you, but I would say the two cathedrals (and the surrounding area, known as the Georgian Quarter), Tate (currently relocated away from the Royal Albert Dock) and the Walker Art Gallery.
St George's Hall is interesting - there are guided tours.
Check the tides and go out of town to Anthony Gormley's Another Place (aka the Iron Men).
If you're interested in the Beatles, there are tours to take in both the Lennon and McCartney houses, Penny Lane, Strawberry Fields etc.
Also out of the city centre, the Palm House in Sefton Park.
Just up the road in Prescot, Shakespeare North Playhouse, which is a replica of a 400 year old wooden cockpit theatre.
Too much for one weekend, but plenty to choose from!
And check the football fixtures for the weekends you might want, as that can push up hotel prices, and affect availability.