Well, the first thing, I think, would be to go around to your own friends, and ask them if they'd like to be "big sisters". Also ask the "little sisters" if they have any relatives or friends who woiuld like to be big sisters to the group. Church social gatherings, synagogue sisterhoods, and other religious and faternal organizations are good places to ask for volunteers, I think. Also, fellow-alumni of your college or high-school, if they still live nearby. If any of the little sisters goes to ballet class or takes piano lessons, or if any of the proposed "big sisters" is taking ballroom dancing, maybe fellow students or teachers would be interested in being "big sisters". And, maybe teachers would welcome the opportunity to be "big sisters", and show themselves to the little sisters as PEOPLE, not just teachers!
Once you get your group started, another good idea would be to have "out of town guests" -- such as, if anyone knows someone who was in New York City, or nearby, on 9/11/01, Holocaust survivors, or spectators during famous trials -- like sepctators at the OJ Simpson trial, or other "we were there" people-- come in and share their experiences with everyone.
As you probably know, there's a "Big Sisters of America" organization, (perhaps alligned with "Big Brothers of America"....I'm not sure), which could help as well -- but I suppose they'd want your group to become a local chapter.
Hope this helps!