The best alternative for a run in central Alexandria outside of the Corniche is to stitch together a route combining Al Shalalat Park, El Qably Park, and a couple of nearby running tracks. Al Shalalat Park is a landscaped park with palm trees and trails around a pond and surviving remnants of the old city walls. Combining with El Khandek El Qably Park across the street for a ~2 km loop. Just across Omar Toson St. from El Qably Park is a nice running track at Alexandria Stadium.
There’s also a running track at the Etihad El Sakandary Club, just east of Al Shalalat Park. Note: might be gated, only open to members.
Longer Run: Head down to the Alexandria Corniche. It’s ~1 km from Al Shalalat Park, using Ali Moustafa Moshrfah St.