Ah... local food or what we call "tipico" Guatemalan food!
Our fav for an authentic meal experience is Rincon Tipico - https://www.tripadvisor.com/Restaurant_Review-g295366-d2422724-Reviews-Rincon_Tipico-Antigua_Sacatepequez_Department.html
It's a few blocks from central park, close to Tanque de Union park. You won't find English menus there and it's mostly visited by locals and a few gringos eating on the cheap. For about Q45 ($5 or $6 bucks, roughly) you will get an entire meal. They will usually have a special of the day but my advice is to skip that. Get the charbroiled chicken that you'll see rotating on the giant rotisserie over open flame. It's amazingly good and comes with a couple of sides of the day and a fresco beverage, which might be Jamaica (hibiscus drink) or something like Tamarindo. You will be served on plain clay plates like locals use in their homes. Women make fresh tortillas on a griddle by the front door as you come in. We've eaten there several times and love it. I recommend Rincon Tipico if you want an authentic food experience vs. risking local street food where you may get sick, which would completely ruin a cruise.
For a more touristy ways to experience Guatemalan food, complete with some smattering of English on menus and much higher prices, I recommend one of these: Los Tres Tiempos - https://www.tripadvisor.com/Restaurant_Review-g295366-d5979554-Reviews-Los_Tres_Tiempos-Antigua_Sacatepequez_Department.html
Very good food and service. Close to the tourist area of central park and arch street. Nice variety on the menu. Fonda de la Calle Real - https://www.tripadvisor.com/Restaurant_Review-g295366-d1464300-Reviews-Fonda_de_la_Calle_Real-Antigua_Sacatepequez_Department.html
Charming Antigua ambience and quite good, with a wide variety of Guatemalan dishes mixed with more familiar American style food. Also near central park.
And the ultimate recommendation for a higher end Guatemalan food experience has to be the hotel restaurant El Refectorio inside Casa Santo Domingo hotel. https://www.tripadvisor.com/Restaurant_Review-g295366-d1090577-Reviews-El_Refectorio-Antigua_Sacatepequez_Department.html
The hotel itself is an amazing attraction, well worth taking an Uber or tuc-tuc over from central park just to walk around. It's a hotel built on the grounds of a historic site where monks used to live, all gorgeous stone and a fountain that is too huge to believe. The food there is excellent and the ambience can't be beat anywhere in Antigua. English is reasonably available (the waiters like to practice their English with you) and you will find a more modern interpretation of native Guatemalan cuisine. You will spend more but visiting Casa Santo Domingo is an experience you won't forget.
If you do go to Casa Santo Domingo hotel, be sure to walk past the restaurant area through to the open areas beyond. There you can wander back to the fountain area, talk to live parrots in the trees (if they are out on display), visit their tiny but delicious chocolatier shop or even tour a Guatemalan art museum (for a small fee).
Hope you love Antigua as much as we do!