Depending on how long ago you were here, you should definitely check out the new visitor center. Huge improvement over the old. Many more artifacts and displays. Cyclorama painting was moved there also. As far as areas around town, 34 north will take you towards Carlisle through orchard country. Nice roads with lots of hills and turns. 30 west will take you towards Chambersburg and through Caledonia State Forest and park. 30 east to Lancaster takes you into Amish country. Short ride south on 15 towards Thurmont, MD is Cunningham Falls State Park.
Touring the battlefield itself can be quite time consuming depending on your interest. Most people only see the area around the High Water Mark and Pickett's Charge as this is the most well known. If you have a real interest, then look for the side roads in park as well.
As far as churches go, there many, many churches in the area. You should not have any trouble finding one for your faith.
While in town, if you happen to like a really good burger, you need to try the Blue & Gray Bar & Grill on center square. They offer about 15 different styles of burgers all named for a Union or Confederate general served with an appropriate flag. They also have great wings and other good food as well.