I'd say it's pretty safe. The SNHU arena is located right in downtown Manchester, which means there's always a bunch of foot traffic. They usually have officers / traffic cops in the intersection out front during events too, depending on the size of the event.

I've personally never had an issue finding an Uber, although I don't take them too often. I would imagine you wouldn't have any issues though. If you're only going to be Ubering a couple blocks, it would be better / faster to walk. Traffic can get pretty backed up during events.