Do I need to hire a "local" web site designer?

depends on what you want done, but mostly or I think you can do a website from anywhere.
have a look at my website, i'm a freelance web & graphic designer.

"yes"

I don't think it needs to be next door to you. But I would definitely hire someone that is near enough for you not to spend a fortune in phone calls, not to mention he should work the during your same working hours. (ie don't hire someone in China if you live in Spain...))

You need to hire someone whose been recommended to you. Doesn't matter where they live as long as you have trust and work with a clearly stated legal contract. If you don't know anyone, your best bet is meeting someone in person in your area.

I'm hiring a programmer over the Internet and we are working together without any problems. I never met him in person and don't even know how he looks like in real life :)
It'a all matter of trust as Nato says.

i agree with jozefk, if you find someone you can trust & you work well together it's worth it! no need then for a local person.

I've had great success working with a fellow member of this very community, who lives thousands of miles away from me and whom I've never met in person, though I'd to. The key is to know the person's skills, an assurance that they're dependable, and that you (literally and figuratively) speak the same language.

I've had nothing but awful experiences with local Web designers. We just don''t have that talent in my town.

So bottom line? Depends.