The house is in a great location - you are on a hill leading from Trapani to Erice, so you have great views down to the sea, absolute privacy and tranquillity. In about 20 minute drive you reach Erice, which is a beautiful historic place but quite busy so you'll appreciate your peaceful terrace on your return. The sunsets there are amazing.
As a one-day trip, I fully recommend the Riserva Naturale orientata dello Zingaro. It's about 1 hour drive from the house - a beautiful coastal walk. Take food for your picnic and set off early to get a parking place.