Actually there are two Rostovs in Russia, the other one is in the south and called Rostov-on-Don. This Rostov is the oldest and Veliky stands for the Great because of its age. It was first mentioned in 862 in the Primary Chronicle, and two centuries later it was joined by Rurik to his Kingdom, since then it became a big political center and the throne of Church. Population of Rostov the Great is small. It is over 30 thousand people.
Rostov has a train station on Moscow - Yaroslavl railway and is served by several trains, Moscow - Yaroslavl expresses and local trains from Yaroslavl to various stations between Rostov and Alexandrov. It is possible to get to Rostov from Moscow by local trains with change in Alexandrov, but check timetable first, because trains from Alexandrov to Yaroslavl sometimes get cancelled recently. Express or morning trains from Moscow seem to be most convinient connection though.
If you're planning to return from Rostov to Moscow by train, be aware of the evening gap in connections - there are no trains between 8pm and 2am, and there might be no tickets on 8pm express and you may spend several not so comfortable hours on the train station at night.
The distance from Moscow is 202km (3 hours).