Union Point and Gazebo New Bern NC – print from Janet’s original. A trip to New Bern isn’t complete without a trip to Union Point Park, which is a scenic six-acre site located at the point of the Neuse and Trent Rivers in historic downtown. The Gazebo – often used for weddings, festivals, and other special events – offers a magnificent and breathtaking view of the waterfront. The park sits at the confluence of the Trent and Neuse Rivers. In the early 1900s the site was a city dump, the Women’s Club took it upon themselves to get it cleaned up. It’s now a jewel of our town.