This was filmed in Wilmington, North Carolina at Screen Gems Studio.
Who is the father of Jen's baby?
The show never explicitly reveals who the father is. It could be Billy.
What happened to Bodie (Bessie's boyfriend)?
He turns up in a few of the seasons, you definitely see him in season 3 and 4. He eventually was said to have taken a job as a chef on a cruise ship to support Bessie & their son, which explained his lengthy absences from Capeside.