Aulani can get crowded on weekends with local visitors, so its advisable to plan any off-site outings on weekend days do avoid that. You will also avoid rush hour traffic by going out on weekend days.
As far as other activities, there's many things that can be recommended but it will depend on your ages, how much time you have, what you like to do, what's important to you. I would recommend a visit to the North Shore for anyone - exploring the area, local dining like Kono's, Matsumoto's, the shrimp trucks. Many people like the Polynesian Cultural Center if they're into history and culture. Diamond Head for hiking. Hanauma Bay for snorkeling. Kualoa Ranch for a variety of things and movie fans. Waikiki for shopping and dining. I'd probably recommend Waikiki to anyone too because its a very different vibe than the rest of the island. Lots of shops and bars/restaurants in walking distance, beautiful views, great people watching.