I'm a Catholic in Burlington but I'm familiar with several churches in the Graham area. I've compiled a list of churches I think you might like.
Good luck! And hope you find what you're looking for.
First Baptist Church, Graham -
Welcome to First Baptist Church of Graham, NC
First United Methodist Church, Graham -
First United Methodist Church of Graham
Graham Presbyterian -
http://www.grahampresbyterian.com/
Bethany Presbyterian, Graham -
Bethany Presbyterian Church - Home Page
Providence United Church of Christ, Graham
These churches are in Burlington and are very popular:
Brookwood Baptist, Burlington -
Brookwood Church (http://brookwoodchurch.com/index.cfm?i=1693 - broken link)
The Episcopal Church of the Holy Comforter, Burlington -
Holy Comforter - Welcome
Trinity Worship Center, 3157 South Church Street, Burlington, NC 27215