We stayed an Agios Prokopios for 10 days with our two kids (10, 12) and two adults. The appartment isn't suited for four people in this combination. There are three proper beds and a sofa to sleep on, which is basically ok. However, the sofa/bed takes up all the space in the living room/kitchen area and there is not really space for dining together as a family at one table. It's very cramped. If you have small kids and they can share the double bed with one adult, it would be ok though. Also, there isn't really enough kitchenware (plates and cutlery) for 4 people. It would be fine for 3 people. You can sit out on the balcony or in the garden, but again, there aren't really tables gib enough for 4 people. Other than that, it is immaculately clean (it's cleaned every day, linens changed every 3 days and towels changed on demand any time) and just as in the pictures. Being in the basement, it's also fairly cool most of the time. The location is perfect, literally 2 minutes walk from the beach and 3-4 minutes into the village center with bars, restaurants, shops etc. If you rent a vehicle, there's a parking lot right behind the house. Be aware that there are strong winds (Meltemi) most of the time on Naxos, so the sea is cooler than expected (but still very pleasant).
Nikos was a very helpful host and lives in the same house, so he's available any time if there are issues.
All in all, an excellent place for 2 or 3 people to stay for a few days or longer. Though we weren't totally happy about the bed/table situation, we still really enjoyed our stay and would recommend staying there any time!