For snacks, I recommend going to Hunan Road and Confucius Temple. There are also some in Xinjiekou. The night view of Confucius Temple is good. For shopping and clothes shopping, go to Xinjiekou, Hunan Road, Shanxi Road, both high and low-end. I don’t know about Sun Yat-sen Mausoleum or the Presidential Palace.
Do you have any interest, but it is unique? The people above mentioned mountain climbing, but I personally don’t think you should climb it. It is available in every place and is very similar.