There is no way skipping Harvard in your itineraries if you are in Boston. However, since the university is not small, I think it is wiser to have yourself a guide.
Just in front of the Harvard Square, you would find Harvard tours which usually started at 10.30am, 11.30am, 1pm and so on. The duration is around 1 hour and cost only USD10.
Harvard Square is just like a market, which is surrounded by cafes, restaurants and shops in this area.
There are starbucks, but if you would like to find yourself somewhere different to chill, then you definitely should try the Crema Cafe.
Yes, Crema Cafe is very famous and also have quite a pretty long line in the morning. They serve great foods and also have a nice atmosphere, enjoy your day in Harvard!