I concur with eschjw. Considering your interests and traveling plans, then recommend staying in or near Gatlinburg.
The fall season is busy and October is the most visited fall month. The beauty of fall and the peak of college football season make the GSMNP a great place to spend clear days and chill in the air evenings.
If you prefer a sense of being away from the village of Gatlinburg, then Tree Tops Resort or Bluegreen are very good choices. We very much prefer Tree Tops but have enjoyed various properties, cabins and hotels and pitched our tent many times thru the years. We also reside close by and day-trip to the GSMNP.
Due to the various elevations within the GSMNP one can find color throughout the month but as noted the highest and best time frame is usually mid October thru the first week of November.
I usually stay in Gatlinburg for several days in the third week of October for CLE. The weekdays are comfortably busy but the nearer the weekend the greater the traffic. The beauty of the GSMNP is that you are only have to select a trail and the crowd is no more. Also visitors really do not get going until around 930 to 10 in the mornings so if you get up and out it is like it is a different place. Dining, walking, driving, getting to trailheads, etc are really easy in the early mornings. Seeing that you are from the Bay area, perhaps traffic will not be an issue to you, but weekends can be jammed. Thus the recommendation of Gatlinburg over Sevierville or Pigeon Forge.
The best dining spots are the many places in the GSMNP. There are some really great day camp areas with tables, restrooms and grills throughout the Park. Many along waterways.
Wildlife can be seen at any time but the mornings and dusk are the highest and best times. The best place for groceries is Food City just north of Gatlinburg proper off of Hwy 321.