The Antigua Central Market is a local hub for shopping. It has seemingly endless stalls of handicrafts, souvenirs, electronics, and clothes. It's a very cheap and good place to go if you need a new phone screen, socks, or other random items that are hard to find in the old city.
They also have a food section where you can try street food like pupusas or tamales.
Remember to bargain! If you are paying face value you are getting ripped off.