Very interesting idea, but not sure Twitter sentiment analysis tells us anything. Most Twitter users don't tweet, and most college-age people are not active Twitter users. Instagram would provide more comprehensive data.

Even then, you have to make a variety of (sometimes shaky) assumptions:

1. The data set is a representative sample

2. Sentiment of social media posts is a good proxy for happiness

3. Machine analysis is sentiment is reliable (i.e. doesn't fail when it encounters sarcasm, which is common on Twitter)

Wondering if you RateMyProf could be a component of your happiness ranking.

ie. look at the average rate my prof rating per school. There's of course room for bias, but schools with higher professor satisfaction may correlate with overall student happiness.

One way to improve this is to look at the confession pages and the meme page data of the universities. Though getting all this data will be cumbersome.