Savaii is the larger, but less developed, of the two main islands of Samoa. Many people say that Savaii is the 'real' Samoa. It is certainly less developed, with no real towns as such, just a series of small villages with people living in traditional huts. You don't have to worry about getting lost on Savaii if you're driving - only one (well-paved) road runs around the island.
Every few miles you will likely pass a colonial-style church, while the coastline will regularly change between volcanic black ash, pristine white sand beaches, and dramatic cliffs. Overall, visit Savai'i if you want a more authentic and unspoiled Samoan experience away from the Internet cafes and McDonald's of Apia.
Circumnavigate the entire island over a few days or a week (although it is possible to do in day) and admire the wonderful lush scenery and contrasting coastline.