DH and I are also not religious. However, we don't have any issues with any religions either, so getting married in a church was no different for us from getting married anywhere else (plus, it comes with a complete lack of familial complaints about not getting married in a church). We chose to get married in the chapel located at the living history site where I worked for a brief time during college. My mother also worked there during her college years and my parents were married in the same chapel. I liked that it was a place with "history", both in general and for our families. Outdoors was not a consideration because we live in Michigan and I've seen far too many outdoor weddings here ruined by the weather. It did, in fact, rain on my wedding day, proving that I made the correct choice.
Our reception was at the large hall associated with the site. Very pretty and historic.