Shennongjia is a vast wilderness area, and what you visit is largely determined by your driver, fellow passengers and available time; however, there are definitely some areas that are worth trying to get to. Seeing the rare golden snub-nosed monkey (川金丝猴, chuān jīnsīhóu) is a highlight for most, and Xiǎolóngtán (小龙潭), about 10km from the entrance, is one place to spot them.
Shénnóngdǐng (神农顶), 20km from the entrance, is the highest peak in the park (3105m) and can be climbed in summer – figure on two to three hours. The wetlands surrounding Dajiu Lake (大九湖, Dàjiǔ Hú; additional ¥60 shuttle bus fee may be in effect) also get high marks from travellers, though this is considerably further away and requires a minimum half-day commitment. Other places of interest include several waterfalls and a stone forest (板壁岩, Bǎnbìyán).
All in all, when the weather is good, the scenery here is spectacular. However, you should always be prepared for mist and rain. In winter snow is common (there's even a mini bunny slope for first-time skiers), and may remain on the ground through April.