This private museum belongs to Francisco Marroquin University. It's located a bit out of the city centre, but in a very nice area. The museum has one of the best collections of existing Mayan pottery. If you want to take photos, you have to pay the supplementary fee (I don't remember the price, but it wasn't much). The hours are Mon to Fri from 9:00 to 17:00, and Saturday until 13:00.
The Guatemala City Railway Museum is a beautiful museum where you"ll find types of historic train cars and restored locomotives. The guided tours are interesting because aside from just providing information, they actually try to recreate scenes and scenarios from history. It's an interesting and different way to spend a morning in Guatemala City!