Shrewsbury lacks a full size decent nightclub. It has a few nice venue's, but nowhere anyone with experience of major urban nightlife will be impressed by. Having said that some of the nicer bars are found down on the riverside. My old favourites used to be Bar 7, and The Armoury.. assuming they're still called that, any taxi drive will know them. Another place I liked was Brady's... next to the train station it's an irish (not really, just claims to be) pub, nothing amazing but did have a free jukebox last time I was there, woo-hoo!
Dress Code: Most places will ask for shoes, but most other things will be ok.
The Wheatsheaf is a pleasant pub located in the centre of town. They have a good selection of beers and friendly service in a warm atmosphere. Sometimes there is live entertainment.