I happen to have graduated from SUNY Albany and lived in Albany, NY for 4 years.
The city is very well organized with police presence in most parts of the city.
In the scarier parts of the Downtown, I can imagine the city getting overwhelmed. But I do not predict we'd be overrun like the RPD was. I'd imagine that the weaponry we have at this point and the ability to communicate locally and globally would prevent the disaster from getting too out of hand.
Of course, the real fear in these scenarios are the riots. Watch the first season of Fear The Walking Dead and you'll see that the fear of being harmed is almost more deadly than the zombies themselves.
As a Resident Evil fan who lived on the Albany campus for years, I was always coming up with ways to fend off zombie outbreaks and that campus is really uniquely built. The original campus was designed to be set in Arizona and has many passages and features that allow wind to be trapped. But it got built in Albany, NY - so the winters become BRUTAL in the quads/dorms. The ice cold wind WHIPS you in the face on a blustery January day. Luckily, beneath all of the dorms and classrooms, a series of tunnels connect everything. Some of them are currently blocked off in the dorms due to a high level of sexual harassment during the late nights when the security is lower - but they exist. And you could easily traverse the entire campus in 15 minutes by using these tunnels. The tunnels have multiple floors as well. At the deepest center of campus, you can go 4-5 floors down underground and find hidden offices and the College Radio Broadcasting Center.
It would be a FUN place to be in any sort of scary situation.