Endorse BRL's Popham comments friendly place, funky finals etc. but here's another thought:
OK so its not really Hampshire and from F'boro you'd have to drive past Popham to get there, but what about Old Sarum? I was down there the other day to visit Littlest Sister Rimmer and found it a very welcoming place (xtra thanks to the folks in the flying club that lent LS Rimmer a headset BTW)