The Place
A bris can take place in any location that the parents desire. Traditionally, a bris took place in the synagogue. However, many people prefer having the bris take place in a home. Others (especially if you are expecting a large crowd) opt for a hotel or other large area.
Traditionally, the bris is held in front of all those present. If the parents don't feel comfortable with doing it that way, the actual circumcision can be held in a side room and the blessings and baby naming done afterwards with all those present.