It's not particularly far from Newcastle center by bus, I'd say 10-15 minutes from what I remember. The #21 bus leaves from Pilgrim St. Timetables at http://www.gonortheast.co.uk./
Also, you can get driving directions at the Angel of the North website.
Apparently it is known localy as Rusty Rita!
I do believe just plain Rusty would be a better name. After careful examination, the Angel is clearly amorphous and sexless, or possibly male. I've had to train myself to say "him" or "it" instead of "her."
Whatever, I like it, a lot.
Easiest = car.
You can get really close to it, you can stand on the feet if you like!
By the way....I remember hearing that it was designed to rust that colour. Thats your fact for the day!