The best way to get from Rome to Tivoli is by Train from Termini station. The rest of the city is easy to reach by bus or underground.
It as even possible to do a lot on foot.
We was coming with train to Rom, it was adventuarally. In Rom the people are driving with little rollers, very great. Are driving to work, for shopping, for culture ...
Almost all modes of transport come to Roma Termini. trains from the Fiumocino Airport, buses, metropolitana, taxis all have their stops here.
Since January 2009, there is a FAST TRAIN (treno ad alta velocità) from MILAN to ROME and it takes only 3,30h (instead of 5 or 6!)