The South East face Whitesides is a great place to hone your long route skills if you are prepared for sometimes long runouts over sometimes dubious gear. Early starts are helpful, if not mandatory, if you are unfamiliar with the routes. Fall, Winter and Early Spring are the best seasons as the weather is "predictable". Summer is tough because of heat and unexpected storms approaching from the Northwest, also retreat is difficult because of the wandering nature of some routes and lack of fixed anchors.
The NW Face of Whitesides also holds adventurous routes as well but sees less traffic than the SE Face. For more info on both faces of Whitesides, consult either Thomas Kelly's The Climbers Guide to North Carolina or Harrison Shull/Yon Lambert's Selected Climbs in North Carolina.
In Winter, Ice Climbing is certainly possible on the NW face. The two classics are Mother Russia and Starshine.
Having said that, Whitesides is adventure climbing at its best and routes such as the OR and Traditions are excellent training for grade III and IV routes in other parts of the country.