Cartago (named for the city of Carthage is a city in Costa Rica. Cartago is a province, canton and a city. This writeup is mostly about the city, although the city of Cartago as I understand it may not accord with strict jurisdictional definitions.
Cartago would generally be considered part of the San Jose region, and it is easy enough to commute between the two cities, but Cartago is actually on the other side of the continental divide from San Jose, on the Atlantic Ocean side. Cartago is also at a higher elevation, around 1450 meters/4800 feet, which is about 200 meters/600 feet higher than San Jose, and usually has noticeably cooler weather, as well as different vegetation. The city of Cartago itself probably has a population of around 100,000 people. (It is difficult to say exactly because parts of the cantons that make up Cartago extend outside of what we would think of as the city. There is a shopping mall, as well as a traditional mercado. There is a fair share of restaurants and shops for locals, but it is not an international tourist destination. The most notable things are the "ruins of Cartago", which was a gigantic church that was destroyed by an earthquake, and a large basilica dedicated to Mary, the Lady of the Angels. Cartago is also the main seat of the Costa Rica Institute of Technology.
Cartago was founded in 1563, and for many years was as important, or more important, than San Jose. In fact, Cartago was the first capital of Costa Rica. Now, the city is basically a suburb San Jose, although one that I feel has a different (and perhaps more traditional) culture than San Jose. In Costa Rica, Cartago is one of my preferred destinations, in part because of the cooler climate, and easy access to rural countryside around the city. Many locals find it curious that I like to visit Cartago, because here, it just seems like another city. But of course, for me, getting to see the bustle of a crowded market, the ruins of an ancient church, and the miles of surrounding the surrounding rain forest and farms, make it an interesting and worthwhile place to visit.