There isn't really that much to the Execa Ruins. When you first arrive by boat from Gale it's a good idea to wander the town clearing the Skeletal Warriors and Fetid Zombies that are around. There's also a Vampire near the South Gate. These Skeletal Warriors are tougher than the ones you've fought throughout the rest of the game, with about twice as many hit points. Don't forget that Fetid Zombies cover you with acid if they attack you, so it's pretty much a necessity to have either Curing Lv.3 or lots of Curing Potions on this island.
In the southeast corner of town are two locked rooms. The western room is empty, but the eastern one contains some Elder Aranea. Just to the east of the room with the Aranea is a secret passage containing a couple Spectres who appear to be guarding a pair of Cursed Boots and a Potion-making Charm.