we plan to stay in Nanjing for several days to 7 days.

I’d like to provide some suggestion:
First of all, I think you can make full use of the 10 days to travel around the places, like Suzhou and Hangzhou, and then you can visit NJ.

Day 1: Find a hotel in Shanghai and spend the last day in Nanjing Rd Pedestrian Street;
Day 2: Yuyuan Garden- Oriental Pearl Tower – the Bund;
Day 3: Disneyland;
Day 4: Xintiandi & Nanjing Road and then take a train to Suzhou;
Day 5: Humble Administrator’s Garden- Suzhou Museum- Tiger Hill
Day 6: take a train to Hangzhou: West Lake - Song Dynasty Town;
Day 7: Take a bus to Wuzhen Water Town;
Day 8: take a train to NJ: Confucius Temple- Qinhuai River- City Wall;
Day 9: Xiaoling Mausoleum of Ming Dynasty- Presidential Palace- Dr. Sun Yat-sen’s Mausoleum.
Day 10: walk around Xinjiekou Pedestrian Street and prepare to leave.

not exact itinerary, only some overall suggestions
I think a 3-day trip is enough for someone coming to the city for the first time.

Dr. Sun Yat-sen Maosoleum, Presidential Palace and Qinhuai River are the top three "must-go" (you may complete these three spots in one day if time is limited).

If you are interested in the history and lifestyle of Republic of China, then Yihe Road and 1912 bar street are good choices(1912 is next to Presidential Palace).

As for Chinese-style architecture, you may enjoy it in the old campuses of NJ University(Gulou), Southeast University(Sipailou) and Normal University(Suiyuan). All these campuses are in use and open to public.

A ride along the Greenroad by the Yangtze River(from Zhongshan Port to Yuzui Wetland Park) will assure you a wonderful afternoon.

Qixia Mountain is too far away from downtown, and no ropeway provided there, though the scenery on the top of it is really charming (if there is no smog of course).

NJ Museum is also recommended, however, it will cost you at least half a day before you can really get something about the city and China from there.

i don't know what season you will come, but try to avoid summer and winter. i nearly forget Laomendong, in fact, I think it's better than Confucius Temple area.