Per capita, Queens has more cemeteries than any other borough (although Staten Island is gaining ground with the Cemetery of the Resurrection). The larger ones like Calvary are fairly easy to see from the BQE and many parts of Hunter's Point and Maspeth, but it's the smaller ones, tucked away in corners sometimes, that I really like.
Prospect Cemetery, by the LIRR tracks in Jamaica, is one of the oldest, with graves going back to 1709. It's part of York College, so there is no access on weekends and holidays.
Two years ago, I bumped into the owner of the Lawrence Family Graveyard in Steinway. It's a private cemetery, and even though he married into the family, the man is doing a great job with the upkeep. He was nice enough to let me in and shoot some pictures. Major Thomas Lawrence was first buried here in 1703. If you go, try to arrange your visit with the owner (who lives next door), otherwise you won't see a whole lot from the street.
A couple of miles southeast, the Moore-Jackson is tucked in between a couple of buildings. During the spring and summer, the trees and shrubbery run amock, giving it quite the wild look. Even though it's more impressive then, you can see the whole graveyard during the winter months.
I could go on and on, and I will. Don't forget to check out the other Lawrence cemetery in Bayside, Flushing Cemetery, the Cornell Graveyard in the Rockaways (do arrange a tour for this one because you won't be able to see zilch from the street). And if you want to see a mini-cemetery, check out cozy Remsen Cemetery near Yellowstone Blvd on Trotting Course Lane in Forest Hills.