If you're reviewing someone's code, do you run/test the code before reviewing the logic? Or do you review logic before running the code?

unit test do the assertion on the result of the code

humans do the assertion on the readability of the code

Always the code. Tests are automated and will fail on checkin.

Sometimes if you have some doubt how things are working or not working I also verify manually how it behaves.

I do this very rarely (few times per year)

I don't run code when I'm doing code reviews, however if I'm doing some QA work I do read the code first. Reason is if I read the code first and find a flaw or think something should be done differently I can inform the dev about that and get those issues resolved first. There's no point in running the code if they're going to have to make code changes first based on those previously mentioned things.