Just walking around North Conway Center for shopping in a beautiful place is fun :) There are great outlets and local shops alike - we like the REI and LL Bean outlets. Check out the town visitors website for some recommendations: https://www.visitmwv.com/shopping?member-village=north-conway
Many of the ski resorts in the White Mountains offer gondola or chairlift rides in the summer for sightseeing. Closest is Cranmore Mountain (chairlift). Others to look at are Loon Mountain, Cannon Mountain, Wildcat Mountain.
There are SO many incredible hikes in the White Mountains. Moderate difficulty hikes nearby include Cathedral Ledge, Black Cap, Boulder Loop trail. Harder hike nearby is Kearsage North. One of our favorite spots is the Willey House in Crawford Notch - just the drive and parking in the parking lot there is worth the trip. You can also head up the trails from Crawford Notch (Mt Webster, Ripley Falls, Arethusa Falls).