Teignmouth AFC is the nearest to my birthplace.... http://teignmouthafc.non-league.org/ Although I follow Torquay Utd's fortunes as they are the nearest professional Club.
Alton Town FC. I used to play for them and there was also the Bass brewery team; played for them too.
Basingstoke Town FC. Still live here now, been to a few games over the years until my Dad started taking me to Southampton games with him!
Blandford United would be my home town club. Slightly further afield would be Poole Town, or if it's a club in the Football League it would be AFC Bournemouth. I have never been to watch any of them!