I took a quick weekend trip (arrived by train Saturday morning and departed Sunday evening) to Nanjing a few months ago and made it to these sites:

1. Purple Mountain - Take the cable car ride; it's relaxing and worth every jiao (really, really long). The view from the top of the mountain's not memorable, even if you get a smog-free day, but the trip's fun. I thought I'd walk down from the top to the mausoleum of Sun Yat-Sen but wasn't able to - the park is huge and trails aren't marked.

2. Yangtze River Bridge - An absolute must-see if you have any interest in Sino-Soviet architecture. You can get onto the span from the stairwells in the supports, or take an elevator up for ~2 RMB. Don't go after dark - you'll miss the great murals/sculptures and the scooter drivers who also use the sidewalk are spectacularly reckless.

3. Presidential Palace - A surprisingly fascinating place. The complex has been practically untouched since abandoned. It's light on propaganda and not visited by the provincial tour group crowds, and you can wander around through the unadulterated buildings at your leisure. Some very decent art deco and international-style architecture there.

Also - I cannot speak highly enough of the Sofitel. It's simultaneously the least expensive one I've ever stayed at (~550 RMB, maybe the least expensive in the whole chain?) and has the nicest rooms (the bathroom alone was about 20 sq meters; the whole room as large as my apartment in Shanghai). The best breakfast in the city too - it's a great deal.