There's a substantial amount of parking on site, give the arena a call and they'll let you know, one way or the other. It's pretty common for showjumpers to stay on site in their horseboxes, or at least it used to be so people overnighting in vehicles won't be an alien concept. Used be plenty of caravans there for the horse show back in time, I expect there's a good share of campers there now.
The public carparks all have height barriers so you'd be restricted to on street parking which is free but for the most part it's not flat, the town square would be the most level but probably a bit busy for overnighting. Station road might be the best bet for on street parking, opposite the mill or outside the recycling center, you won't be outside anybody's house so to speak. If it's a Saturday night, you'd probably be ok right in front of the mill on station road but you'll be in the way on any morning other than a Sunday.
Corkerys bar has a carpark to the rear, you could give them a call in advance if there was no luck at the arena. None of the other bars have carparks.
