Caernarfon has already been mentioned, but just to add that just under the final approach for runway 26 there is a caravan site called Morfa Lodge where you can rent a dog friendly static caravan. Walk to the site is therefore just a couple of minutes.
Other than that the airfield is remote from shops and other facilities but it is served by local bus and taxis to get into Caernarfon (approx 5 miles away)