Like most everything else in confined Montserrat, dining opportunties were also quite limited and packed to the max!
In a section called the Placa de la Creu which faces the main road below the actual sites is a conglomeration of eateries which take on a fast-foods, high school snack bar setting. Bocadillo/sandwiches, chips, fries, fruits, ice creams, sodas and other drinks and such are sold at various counters for an above average cost with a below average quality. Within the dining area, you'll be lucky to find a spot to sit and will likely have to clear the trays, dishes, etc. from a table once a chair opens up.
Within the same cafeteria area, and in a couple of other larger locations within the compound, are gift shops selling many momentos from the Montserrat area, but you'd be wise to check out their bottled liquers made here and sold in various sized bottles. I purchased some of the 'Crema Catalana de Montserrat' made from milk, sugar, eggs, flan and with a hint of lime which was 32-proof Gran Licor and the closest to anything I've found like Jamaican Rum Cream without actually being on the island. Airplane sized "bottled shots" also made great souvenir gifts for relatively little cost.
Further out along the same main road below and across from the basilica is another group of unsuspecting cafeterias built within a complex that hangs out over the side of the mountain. These are more full service cafeterias with entree elections and of course, higher prices. This entire area definitely had a more "official" approach to it in accomodating tour buses and also appearing to have conference centers. Outside the dining areas are balconies that lead down into mountainside gardens which have excellent views.
There's also a restaurant in one of the hotels.
Once you reach the top of the funicular, there's a nature center which has vending machines with drinks. I had some fruit in my bag and if I'd known conditions would be as crowded, limited, and somewhat expensive as they were, I'd have surely picked up some food before leaving the city and quietly dined atop the mountain where my only interruption and distraction would have been looking in a different direction and being mesmerized by what I saw.