The Palatine is the most important of the seven hills of Rome, chosen by Romulus to found the city and later turned into the site of the Palaces of the Emperors.
The hill is accessible with the same ticket as the Colosseum, and, in my opinion, it is the most important of the three sites included: Colosseum, Roman Forum, and Palatine.
That's because you can see the entire archaeological site from a high point and the whole city.
Moreover, it includes the visit to the Palatine Museum, which gives an idea of the astonishing decorations which once adorned the palaces and shows the history of Rome from its foundation to the emperors.
The best-preserved part of the palace will be the so-called 'Stadium' which was the personal chariot races track of the emperors, part of the Domus Augustana built by Emperor Domitian for his private quarters. From the same palace, you'll have the chance to view from a high vantage point the Circus Maximus, the oldest and biggest circus for chariot races in Rome, and to visit the remains of the central palace is, the Domus Flavia, still holding the ruins of the dining room and the throne hall of the Emperors.
If you come from the Colosseum, you can access the Palatine hill from via di San Gregorio, just behind the Arch of Constantine, or from the Arch of Titus.
In spring, I took my mum up on the Palatine. I brought some panini (sandwiches) and had a great picnic on the benches of the Horti Farnesiani. So you can do the same if you like. Don't get too complicated, and don't bring too much stuff; the guards might not appreciate your professional picnic style. Remember that you are in a 2000 years old archaeological area, in any case.
There is not a cafeteria on Palatine hill or in the below Roman Forum, but you can find public fountains (called by the Romans big noses) if you are thirsty. The water is fresh, always running, and safe.
If you are lucky as my tourists three days ago, you will meet black rabbits in the bushes of the Horti Farnesiani.