Best Hop on Hop off bus in Rome?
None. They don't go everywhere you want to go or get very close to some sights/sites due to narrow streets. Just walk or use public transportation.
For the core or central part of Rome, they are limited because of traffic and congestion. However, we did enjoy that archaeology bus that looped out through the Apian Way, catacombs, and a number of other outlying sites. It work very well for that route.