I would recommend taking tour buses. I don't mean the public buses you'll see which are crazily decorated old american school buses. I mean smaller buses (often minibuses) that you can arrange from a tour office. There are plenty of these in all the major towns. They are designed to take you to all the attractions, and they're usually pretty damn cheap.

Antigua is a cool town, that maybe slightly overrun with tourists, but it's an excellent base to explore the surrounding area. I would personally recommend a visit up Volcano Pacaya (bring sturdy shoes for the lava!) and a trip to Lake Atitlan. Tikal in the north is amazing, and the Rio Dulce.

Everyone always mentions the market of Chichicastenango, but I found it quite tame and boring to be honest.

Anyway, have a great time!