U can learn Mandarin while traveling around shanghai.
If u have a very long holiday in China,like one month, u can also travel around
Except that u can also experience the local culture in SH,what do u think?
So u can find a very good teacher also a guide tutor so that u can also learn Mandarin
and Culture from him or her,and go around the cities.
In shanghai,there are a lot of sights like Xin tian di ,Yuyuan Garden, Science Museum,
Nanjing road ,iDuolun road, Qibao ancient town,Fuxing Park,Hengshan road etc.
And if u have time ,u can also go to suzhou or hangzhou for a one day trip.
Hope u have a really good time there. If you stay in Shanghai,you c an choose Mandarin Garden
that is a biggest mandarin school in Shanghai,
Study Tour is their advantage program, this program satisfy your entire requirement.