The Crown Tavern, The Old Fountain and the Eagle are all nice pubs. Don't know about veggie food. Mainly just avoid anywhere with TVs.
Slightly different option would be the Barbican. Lots of comfy seating dotted around, people doing lots of stuff including games and a few bars to choose from.
Others probably have a better idea but I'm thinking of around the foyer area, there are plenty of chairs, tables, armchairs and sofas scattered around.
This kind of area:
Go and get a drink from one of the big foyer bars and take it back to where you're sitting
The Crown Tavern, The Old Fountain and the Eagle are all nice pubs. Don't know about veggie food. Mainly just avoid anywhere with TVs.
Slightly different option would be the Barbican. Lots of comfy seating dotted around, people doing lots of stuff including games and a few bars to choose from.