You could take a boat along the river Deva, but since the river silted up back in the 1600's, that's less of an option. The river's silting, combined with Chester's support of Charles I (the wrong choice) in the English Civil War, led to Chester's marginalization and lack of industrialization. For centuries, the town was left behind.
Of course, in retrospect, this was a very good thing. Chester does not suffer the pollution and crime of neighboring cities in the Northeast. But it does mean that to get to Chester by train, you'll have to change lines at Crewe, a rather sketchy industrial town east of Chester.
Open-top BUS sightseeing tours - last 55 minutes but your ticket is valid all day so you may get on and off the tour as you please. Frequent departures every day from various stops around the city including the Station, the River Dee, Town Hall and Lower Bridge Street. However Chester is fairly compact and it does not take long to get anywhere.
Chester Station is probably about a 10 minute walk from the city centre. There are quite a few shops on the concourse as well as a nice bar/cafe.
There is a new way to see Chester - from a 1911 vintage bus. The staff wear period costume and it takes in all the sites.
Take a cruise up the River Dee.
1/2 nour cruise Adults £6.00
Pay on board.