How widely is Mandarin used in Nanjing?
Nanjing has a very good education environment. Most of the famous universities of Jiangsu province locate at Nanjing. So Mandarin is wildly used in Nanjing and most of the young people are well educated there (this means they can speak English). They may speak Nanjing dialect with their parents and friends, but they can also switch to Mandarin as soon as they find you are speaking Mandarin. Additionally, my hometown is a small city adjacent with Nanjing and our dialect is very close to Nanjing dialect, but I found both these two dialects are quite close to Mandarin. So just go there with your Mandarin, don't worry! (I know little about French but I still went to the Quebec city last year!). And If you found some trouble, ask for help to the young people there, they can speak Mandarin and even English!

By the way, the 'l' and 'n' issue you referred is true about the dialect. However, most of Nanjing people won't do this when they are trying to speak Mandarin seriously.