Duluth would be the closest. Lots of good shopping. Stay at Canal Park, shop at Canal Park. Right on Lake Superior.
After that, you really need to go to Grand Marais (quite a bit further). I love Grand Marais...terrific shopping, beautiful city, all within walking distance. It's about 2 hours north of Duluth.
Bluefin in Tofte is very nice, and there is a little bit of shopping right there, or you could drive up to Grand Marais...it would take about 30 minutes. Bluefin is my favorite place to stay on the north shore.
My thoughts. Feel free to ask more, as I have spent lots of time up and down the shore.