I haven't stayed at either hotel, however your probably best off at the Faros, closer to the beach and out of the main strip. The main strip can be very loud even out of season. You will find nice restaurants everywhere. Nikitas Italian is lovely, service not the best but the food second to none. Plenty of other lovely restaurants, lots of meze which is delicious. Most restaurants you can get starter and a main with cocktail or alcoholic drink for about £20-£25. I would suggest hiring a car, I used sixt which is easily findable from Larnaca airport. It does make getting to places so much easier as not everything is walking distance from those hotels. For a medium sized car for 4 people it was around £24 each. Ayia Napa was pretty clean, however going up the strip at around 11pm may tell a different story lol. Enjoy, I came back on Wednesday and loved every minute.
we stayed at Napa Plaza for our 25th and were a bit concerned about noise before we got there, but there was no need to worry ,we never heard a sound from the square or strip. The hotel was spotless and the ambience around the pool served for a very relaxing break. True the Faros is nearer beach, but Napa Plaza is only a 10 minute stroll, and its adults only in Plaza .
I have just booked Napa Plaza for next year, the reviews of the hotel are extremely good and they say you can’t hear anything once inside. I know the area where it is as I have been a few times and it’s very handy with everything around you