Use web-based APIs to find and analyze mentions of names of movie stars on twitter, facebook, blogs, and other social media websites. Use the collected data to do interesting data visualizations.
For example: Draw stock-market style graphs of popularity of the top stars in the last year. Or show relative popularity of stars by type of social media (facebook vs twitter). Find interesting patterns in the data - is social media popularity of stars correlated with box office performance of their movies? Can you predict the box office performance of a movie based on social media popularity in the week before the movie's release?
To help with data collection and analysis, a database of movie stars, with their twitter handles, facebook pages, blogs, imdb profiles, wikipedia page links, biographical info, and recent movies can be made available to you.
Note: the core engine developed as part of this can be used for many things other than movie stars; for example mobile phone models and other products.