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I'd second Browns, great food and happy to serve coffee or alcohol at any time (they also do a nice breakfast!). The door policy includes a complete ban on children, so if any ones has little ones, you won't get in
Nice pubs within 5 mins walking distance from the registry office are: Inspire (just over the rd to the left- a bar at the bottom of a spire ruin) Browns - lovely contemporary bar with a nice atmosphere. However it has a very strict door policy, but I'm sure you wouldn't be challenged (they won't allow chav looking types) A very new place has just opened next to the Cathedral called The Establishment, my dad raves about the place (it was once Coventry's County Court) Just over the road from the registry office is The Squirrel- pleasant enough during the day as it is frequented my many of the local office workers such as solicitors, but not sure what it's like in the evenings.
We are going to an afternoon Wedding soon. The evening plans are a little sketchy and we know there will be a meal in a local restaurant (not sure what time or where) and the young Bride and Groom will be with many of their 20 year old something friends, so us old farts might need to gracefully leave them to it at some point. We'd possibly like the option to go to a half decent pub or bar. Any recommendations, thankfully received.