The key to saving money on museums, archaeological sites, and transportation in Rome is to purchase "city cards" from the city of Rome. Budget Travel outlines how you can save using three different packages.
1. The Roma Pass (20 Euros) gets you into two museums/sites and discounts at various other sites and events and unlimited entry on buses and metros for three days.
2. The Roma Piu Pass (25 Euros) also offers the above perks but expands into regional trains and buses.
3. The Roma Archaeologia Card (22 Euros) gets you into an extensive list of ancient sites for seven days.
Budget Travel reminds you that many sites are closed on Mondays, so plan ahead.