The third mountain (besides Popo and Izta) just outside Puebla is La Malinche. It’s about an hour away by car, or a bit more by bus.
La Malinche is covered in pine forests and makes a beautiful day trip. You can run or bike on the flatter roads and trails that cross it, or hike straight up to the peak. The ascent takes about four hours; the first part is in the pine forest, and the second part is above the tree line and includes scrambling over a rock avalanche. It’s worth the effort to get to the top, which provides views far across Puebla and Tlaxcala. If it’s a clear day, you’ll see Popo and Izta on the horizon as well.