If you're looking for actual day trips from Rome, heed the above advice and stick to places nearby.
Ostia Antica, the ruins of an ancient port city, is a good day trip from Rome. Unless you want to spend the time required to visit Pompeii properly on your upcoming trip, consider Ostia Antica as a worthy substitute.
In Rome itself, I agree that by far the best ways to get around are walking, subway, bus, and taxi. You have to learn a new way of crossing the street as a pedestrian though. Different driving habits and those pesky Vespas (motorbikes) throw your timing off when you try to cross!
Kathy