The Arco de Santa Catarina is a very famous landmark. Built in 1694 (and rebuilt in the 19th century), this arch was one of the few structures in town that withstood the 1773 quake. While in Antigua, it will be hard to miss the arches, as they are a very noticeable feature in a popular part of town. While I was there, there was a live concert under the arches one night with great music.
This small city musueum is located in the Ayuntamiento on the north side of parque central. It is inexpensive and has 4-5 rooms of artifacts from the city.
This parque is flanked by San Pedro Church and the Ruins of Santa Clara. In the park is a unique structure the Tanque, a structure used as a washhouse to this day for local women.
There are some beautiful old buildings in the town. Be sure to walk around and really get a feel for the place.