Chester during and after the races will be rammed, has the organiser booked the restaurant and any of the bars? Some bars will operate a guest list during a race meeting such as Bar lounge on Watergate Street. For that reason I would always eat out of town when the races are on. There is always trouble after the meets, whether that is more or less than any other city centre on a Saturday night, who knows.
The Architect is excellent and during the races they have a temporary bar in the garden overlooking the race course. Same with the Abode hotel during the races which is also next door to the race course
There is a selection of bars including slug and Lettuce, chain stuff or as other have mentioned odd fellows or the commercial. Worth a try but at the other end of town is Harkers down by the canal and close to the train station or try the Chester Church which has just opened behind the Blackhouse grill. Heard a couple of good reports but not tried it myself yet. the Falcon pub on Lower bridge street for Sam Smiths is ok if you are looking for something traditional.
There will be plenty of mutton dressed up that for sure and some interesting sights
Woody, I'm a Yorkshire man who's lived in Chester for the Last 15 year, you'll be fine, just don't try the bow and arrow trick, only works on market days