If you can i would use public transport to get into Chester as there are limited places to park and parking is quite expensive.
You can park on the racecourse at the weekend for £4.50 (obviously when the racing isn't on) and is where I tend to park, failing that there are 2 park and ride stations with buses at regular intervals.
if coming to Chester by car the long stay carpark by the county hall and chester castle near the river is best cost £3.00 for 6 hours .the north gate carpark for long stay is limited to 3hours for £3.00
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.
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.