Agreed that a week in Chiapas isn´t very long at all, but a week in Palenque alone might be a challenge, unless you really like getting off the beaten path. I´ve always stayed in the pueblo of Palenque and liked it; lots of services, and historical church, museo, mercado, and sports fields busy with locals in the evening. If you do want to visit San Cristobal de las Casas, there are a lot of threads about that place and nearby attractions. Since you like falls, I´ll mention El Chiflon which I believe are the biggest falls in Mexico, near Comitan de Dominguez, a day trip from San Cristobal de las Casas.
I´m reading a lot of comments about taxis, buses, and tours, yet you mentioned ¨no unlocked cars¨ in your opening post. If you´re going to rent a car, please make that explicit.