Quick answer: In Godalming you can play board games at Wayfarer's Rest (board game café).
Wayfarer's Rest on the High Street is a proper board game café: book a table and pick from the library, or come to the open Boardgame Club on Thursday nights. It also runs roleplaying and Blood on the Clocktower nights. Guildford is a few minutes up the line if you want another option.
A board game café on the High Street with a games library, bookable tables and a packed events list, from roleplaying one-shots to Blood on the Clocktower. Every Thursday from 7pm to 10pm there's an open Boardgame Club night: turn up, find a table and try something new, or bring your own. Under-18s need a parent or guardian with them in the evening club.
Where
46 High Street, Godalming, GU7 1DY
When
Monday 10am to 5pm, Tuesday to Thursday 10am to 10pm, Friday and Saturday 10am to 11pm, Sunday 11am to 7pm
Cost
Tables from £3 to book. Thursday Boardgame Club £8