The entire North Shore is a trip in itself. The city of Duluth is great, but it can be pricy especially in Canal Park. There are many state parks along the North Shore, most with great hiking areas and waterfalls. If you can make your way up to Lutsen Mountain, they have a nice alpine slide and some great views of the lake.
My personal favorite waterfall is Devil's Kettle in Magney State Park. This is a dual waterfall where nobody knew where one side of the waterfall emptied out until the last few years. The waterfall appears to fall into a hole and
disapear. It's quite a drive from Duluth, but one could easily spend an entire week just on the North Shore