Sorry cannot help with Winchester except BTFon/OpenZone operates in Costa Coffee.
Alresford - Caracoli posh coffee shop on Broad Street. No password.
Bighton (3 miles from Alresford) - The Three Horsehoes. I meet Ecademy friends there on third Wednesday of the month to look at what is new on the web. Ask Margaret for the password.
We have seen a wifi sticker on the window of The Albion near the station. I'll have a look and see what the deal is. I've never been to the pub so i don't really know what it's like.