Is it safe going to Best Buy in the Nassau Mall as it looks very trashy and run down.

Yes it is safe

They were renovating recently but it's pretty much completed now

Its extremely safe. You must have seen the rush it handles during the black friday sales. I have visited during otther days too and didnt feel anything unsafe. I bought tv, headphones and some more stuff to my satisfaction.

Pretty safe. Looks like a pretty modern Best Buy. No problems getting in or out.