I run or walk or ride through one or another cemetery near me just about every day.
While my Dad is not buried in either cemetery, I always "talk" to him a bit when I go through. I find cemeteries to be very peaceful and soothing places and always have, and it feels good to go through the cemetery and put the trials and tribulations of my day into perspective. There is a section of massed Spanish Flu victims from a century ago in one cemetery, which always touches me. Though I don't work with infectious diseases, my mom did a lot of historical research on social effects of Spanish Flu; so it feels important to me to acknowledge those small, generic, cheap, massed gravestones every time.
I'm always very careful to avoid mourners. When there is an internment going on, I stay out of the cemetery entirely.
Often there are other people going through, and I've noticed that as a whole they are also generally very respectful.
Cemeteries are sacred spaces, never forget that as you go through. I see no problem running through the one near your apartment as long as you are respectful. (and say a little prayer if you are so inclined)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson