Hell, Fanny!
It takes 10 hour by bullet train from Beijing to Shanghai. Yes, it is possible to visit these two cities in a week. Do you asking for rental car to go from Beijing to Shanghai or get around the city?! Shanghai and Beijing has manu iniversities, many of them are top in the nation. If you mean this, you can visit Beijing University and Tsinghua University in Beijing, Fudan University and Shanghai Foreign Language University, etc. Hope this helps.