In the Tor Vergata area there are some hotels and accommodation possibilities. One quite good can be the Campus X Roma,  where many students live and is connected with the faculty by a shuttle bus but also at a walking distance of 20 minutes.

Nevertheless, it is also suggested to take an accommodation in the city. The better is to select solutions along the metro A line. In this way you will be in between downtown and Tor Vergata, so that if in the evening you want to make a walk you are close to the city center.

The historical center of Rome is delimited by the Aurelian walls. San Giovanni metro station is exactly on the boundary. From San Giovanni area, you can reach Tor Vergata in 35 minutes (with public transportation) while you are close to Rome Cathedral (San Giovanni, very beautiful), 10-15 minutes walking from Colosseum, three metro stations from Roma Termini rail station (the biggest in Rome), six metro stations from Piazza di Spagna and Trinità dei Monti (one of the most attractive and breathtaking places in Rome). Just at metro station Manzoni there are many hotels. Manzoni is one stop from San Giovanni towards city center and 10 minutes walking distance from the Colosseum (reachable also with a Tram in three stops).

Looking at the several portals like or on google you can find plenty of solutions.

In Rome the choice of hotels is so large and the ratio costs/quality is so variable that everyone can find the right solutions for him/herself at personal leisure. There are also a lot of bed and breakfast for example in zones closer to Tor Vergata (for example Cinecittà area or Colli Albani area) that are along the metro A line (so that downtown is easily and quickly reachable).