You may want to start out with the Melekite Rite. They follow the Byzantine Rite, and come from the Middle East, so you will be able to hear the Pater, (Our Father) in Aramaic, the language our Lord firsts offered the prayer in. The Cathedral Churches usually have more liturgical services, (and longer ones) as they are the seat of the Bishop.
Annunciation Cathedral, 7 VFW Parkway, Roslindale, MA 02131
St. Joseph, 241 Hampshire Street, Lawrence, MA 01841
Our Lady of Perpetual Help, 256 Hamilton Street, Worcester, MA 01604