If you mean a public library, then it's an errand. If it's a company library, then it's a next action at work. If you need a significant block of time to do it, it may be a calendar item. However, if you could not walk into the library right now and do it, then it's not a next action yet, and you need to clarify what the real next action is.
It's much like "Buy milk at store." It's going to mean different things to different people. Maybe you're at the library weekly anyway, and just need to be reminded of it then. Maybe your next action is "Schedule trip to the library." And numerous other possibilities besides.
I would either make the Library visit an errand or an agenda action item. Also, since it is tied to a location, this may need to be scheduled and would then be on your calendar. If it is on your calendar then that could be your next action and it won't be on a list.
I realized in reading through this that I had placed the appt on my calendar, so it does not need to go on a list and my calendar, which is different from how I've done this in the past. Thanks again.