El Correo, Antigua's main post office, is across from the bus station. You can drop off your letters here, or ask the staff at your hotel to mail them for you. For packages try Envíos Etc.
All the villages in the Western Highlands have branches of El Correo, Guatemala's post office, but you are probably better off posting your letters from the larger towns, or better yet, back in Guatemala City. If you are sending something valuable, go with DHL, with branches in Panajachel and Quetzaltenango, or one of the local companies that will ship packages. Alternativas is in Quetzaltenango, and Get Guated Out is in Panajachel.
Envíos Etc. (3 Av. Norte 26).
Alternativas (16 Av. 3-35, Zona 3, Quetzaltenango). DHL (C. Santander, Panajachel. 7762-2333.)
Get Guated Out (Comercial Pueblito, upstairs, Panajachel).
El Correo (4 C. Poniente and Calzada Santa Lucía. 7832-0485).
Chichicastenango (7 Av. 8-47). Panajachel (Cs. Santander and 5 de Febrero). Quetzaltenango (15 Av. and 4 C., Zona 1).