I would think that for what you are looking for the best time would be mid to late September or very early October. May would probably be good too but sometimes it can be a bit rainy or early hot.
The nicest units are Regal Vistas. Although not all the units have great views. But some are very nice. Going anytime other than summer and week 51 and 52, the whole resort is going to be only 30-75% booked. So if you end up somewhere that you don't like, within that section you could probably ask and more to a different unit.
The next level down would be Woodstone and Summit. Summit has better view but more stairs and hills. Mountainside would probably be the next down although in a 2 br probably more open and spacious. Not that Summit and Woodstone are cramped, they just made odd layout choices. Mountainside is more like a cabin in the woods vs an apartment/condo either on a mountain (Summit) or overlooking golf and parking lot (Woodstone). The next level would be Shenandoah which I didn't like mainly because it was the first place I stayed in and I had a unit with about 40 stairs to get to the front door up a hill and then one bedroom was up a full flight of stairs and the other bedroom was down a flight of stairs with the living room, kitchen, and dining room on the level of the front door. Eagle Trace would be next and the lowest would be Eagle Trace at Killy Courts and the hotels which I hear are awful.