Keep in mind also that the vast majority of mass shootings in the US happen by people who are mentally ill. For instance, most school shootings are done by former students who believe the school ruined their life in some way and want revenge on the school. I do think nowhere is safe from a shooting, but we do see time and time again the same types of places get targeted (schools, supermarkets, places of worship, nightclubs, etc.). I also agree with what
@Arizona Docent said about the National Zoo. If a zoo shooting was to take place (and I hope it doesn't), the most likely zoos are ones that are free and don't have security checks, such as Smithsonian National Zoo, Saint Louis Zoo, Lincoln Park Zoo, etc. Having to pay to get in wouldn't stop a shooting from happening, but that is one more obstacle making it less likely to happen. You also have to keep in mind that most shootings happen for two reasons: wanting to kill the most people possible, or wanting to kill a certain type of person. The first type is where you get shootings at supermarkets, bars, malls, and other places with a lot of people close together. It would be absurd for someone who wants to kill the most people possible to shoot up a zoo, there are places with much bigger crowds. The second type is where you get most of your school shootings, religious fanatics shooting up a church or temple, etc. I also don't really see this happening at a zoo. As much as we dislike PETA and other activist groups, they are not terrorists. I highly doubt you are going to see an Animal Rights group shoot up a zoo, it just doesn't make sense.
On a completely different note, when I started volunteering at my local zoo, one of the first things we went over were all the different drills/emergency scenarios. We went through all the scenarios one would expect- escapes if dangerous or non-dangerous animals, fires, missing child (the only one I've ever actually seen in five years), first aid emergencies, etc. They also covered one for shooter in zoo. As unlikely as it is, shooter in zoo is something there is an actual plan for by a lot of institutions, which while it wouldn't stop a shooting, is integral to limiting the loss of life.