There are a few old fashioned boozers next to the Ship on Briggate, The Packhorse, The Angel and Whitelocks. So if you get time you could try these. Whitelocks is a favourite with many.
If you are staying longer in Leeds you could try the Adelphi (lower Briggate/Hunslet Rd), The Victoria (behind the town hall) or the Palace (next to Leeds Parish Church now known as Leeds Minster).
These are all traditional Pubs if you want more Gastro Pubs or cheap as chips ones let me know.

There are lots of nice places to eat too. So excited that Leonard is coming to Leeds.