Antigua has many museums worth a visit, but perhaps the best place to start is this historic building constructed in 1558, now a UNESCO World Heritage site. Originally a government and military headquarters, it still houses regional administrative and tourism offices. There's also a museum that features artifacts of indigenous, colonial and church heritages. Especially striking is the arrangement of native artifacts in the courtyard.
If you go:
The palace overlooks Parque Central, the hub of the city, and a great place to hang out and soak in the sights and sounds.
Links:

5A Calle Poniente
Antigua, Sacatepequez 3001 Guatemala