I am not sure if this is what you are looking for but here is what we have done that helps build community but I wouldn’t necessarily call them a team building exercises.
1 - Morning Teas - We have about 20 people and once a week someone will bring/make morning tea for everyone.
2 - We entered a team into a 100km walk to fundraise for charity and the weekly training was a really good time to chat about life rather than work.
3 - DDO - I will organise Designer Day Outs where we go and visit a range of different places that are not in the same industry but sort of relate to what we are trying to achieve, or to inspire us, or to find out about processes, or because it relates to our target customer. For example a design studio, high end furniture shops, art places, local craftsmen.
Cheers
MAS