A difficult question indeed! There are so many incredible and intriguing actors in this franchise. My friend, who has met many of them at Comic Cons (I know it is hardly a benchmark of time spent getting to know the actors), stated that John Rhys Davis is one actor you should try to met, if you can.
But for me? Sean Astin. Samwise has always been my favourite character from the books, and Sean played him to perfection. I have also read his book about the 'hobbit' experience, and would love to meet this incredible actor in person.
Christopher Lee possibly but I have to admit the idea does not appeal to me at all I doubt I'd cross the street to meet any actors or actresses.
Probably either Viggo Mortensen or Ian McKellen. I think my spouse's choice would definitely be Sir Ian.