I guess it would depend on your interests and the time of year. In early June, if everything is coming into bloom I'm heading to Tivoli and Villa D'Este - it's beautiful, fragrant, and the air is "cooler" from all the fountains!
If it's more an off-season, or you enjoy climbing through ancient ruins, then you must see Ostia Antica. I think the ruins there are better preserved (and closer!) than Pompeii!
Claire has some great recommendations, especially the beaches... which are quite different than US beaches! There are just too many choices close to Rome!
Ciao,
Ron