Some bars worth checking out at the east of the town (the town centre is pretty small anyway) ...
Slug & Lettuce - bridge street, good place to have a few beers early on, busy and lots of hen parties generally starting out
Weighing Room (rebranded as Dirty Dogs) - off bridge street on commonhall street, can be quiet but has a great patio area and can be a great place if it's busy
Bar Lounge - eastgate street, great outside area and vibrant
Kuckoo - eastgate street, excellent cocktail bar
Eastgate street generally has a few bars which you can try also like Watergates ...
The Vic at the top of bridge street is quirky but it backs onto a courtyard that also services the Commercial and Amber Kiubge, another popular bar, these two backing onto the same courtyard makes for a great atmosphere especially on a summers evening and when they have a band playing - not sure about this weekend on that score.
On Godstall Lane you have Duttons, can be quiet sometimes but has a good atmosphere and used to be my favourite bar.
Other bars further into town include the Pitcher and Piano on St Johns Street, which is large and gets very busy, this is on the same street as the main nightclub called Cruise - which you may want to end up in.
A bar you have to try is The Church, tucked away on Volunteer street (basically below the large Grosvenor shopping centre multi-storey car park which Matt may have been referring too). This bar is a converted church and is massive and very good with a large outside area.
Off the beaten track you have Telfords Warehouse which is a little way out but walkable and on Northgate street you have a couple of more 'lively' working class pubs but Alexanders is worth a look if you fancy comedy on a Saturday - they have a comedy night from about 9

0 till late (3 acts) but you have to pay to get in and need to be quiet - hmmm maybe not the best place then.
Hoole Village is walkable and at the railway station end of town, lots of bars and pubs but I haven't been there much.
It's a fun night out in Chester and with it being a small place you'll be able to find your own path without being out of a bar for long, if it's a sunny weekend - even better. Plenty of nice eating places too.