If you're interested in slightly more peripheral Roman history (or a fan of Lindsey Davis's books about imperial Roman private detective Marcus Didius Falco - one of her books is set here), then a visit to Ostia Antica is well worth it. The former port of the ancient city is a very interesting and well-signed site, with very substantial remains which compare with those of Pompeii in many respects  -  there is still an enormous amount above ground, and several buildings enable you to climb to the top and survey the very extensive city. No massive crowds, and you are able to wander at will and soak up the atmosphere.

Although well outside Rome, it is the easiest place in the world to get to. If you're arriving by ship, from the port of Civitavecchia, take the train to Ostiense station and proceed through the tunnels, following the Metro signs. If you're in Rome, take the Metro to the "Piramide" stop. At that station (the two are interlinked) either buy a metro ticket or use the one you already have, and follow the signs for the suburban train to Ostia Antica (Roma - Lido railway). The trains are frequent, the journey is about 30 minutes, the stop is clearly marked, and the ruins are a two-minute walk from the station.