6 million tourist can't be wrong! I've lived in Chester all my life and I appreciate it more and more as time goes on.
Places you must see include -

Chester Zoo - the largest and best in Britain.
The Roman City Walls - nearly 2 miles long and circling the city.
The Cathedral - it's free to enter, dating from 1092, it's the 4th most visited Cathedral in the country with over 1,000,00 vistors per year.
Roodee racecourse - the oldest in Britain.
Roman Ampitheatre - the largest uncovered in Britain.
The Eastgate Clock - Victorian, and the most photographed clock in Britain after Big Ben.

The shopping is superb, Chester was voted the 4th best shopping City in Britain - the Grosvenor Precient is covered and contains God knows how many shops! along the main street it is 2 tiered and called The Rows.
We have a Town Crier and he does his 'business' every day in summer by The Cross.
The Restaurants have improved greatly in the past 10 years and now we have a great choice ranging from Japanese to Italian and all in between.

Chester is situated on the River Dee and you can walk along the Groves and into the Grosvenor Park where in July they are holding a Music Festival including the Saw Doctors and Jools Holland. You can also take boatrides day or night on The Lady Diana or The Mark Twain.
As for accomodation - if you're loaded, you can stay in The Grosvenor Hotel right in the heart of the city or there are hundreds of less posh places, many are on Hoole Road which is the main road into the city from the M53.

A bit of trivia - the country's richest man - The Duke of Westminster, lives in Chester at Eaton Hall.
Chester is also the gateway to Wales - Snowdonia is only 45 minutes away.

By the way, if you come to Chester and need a Taxi, ring KingKab on 01244 343434, it has over 200 cabs - that was an unashamed plug.....I work for them!!