I've boated lake Superior quite a bit. I wouldn't recommend the north shore. Not a lot to do and not many places to run for cover if the weather turns sour on you. And trust me if it gets nasty that CV23 will feel really small quick. I ran my 23' Larson Hampton cuddy from Barkers Island in Duluth over the the Apostles and back but I wouldn't recommend that to anyone without a lot of experience on the lake. Your better offer just trailering over to Bayfield and exploring the Apostle Islands from there. You can also slip the boat in a marina and use it as a hotel room which is what I've always done. As Jason already said there are lighthouses, hiking trails, docks to tie to, and beautiful sandy beaches you can enjoy in the Apostles.
Before leaving I'd put a ship to shore radio in the boat, get some good nautical maps of the area, and bring someone along in another boat if possible for safety. If something happens and you have to get in that water you've got about 10 minutes before hypothermia sets in. There is also a book written by Bonnie Dahl called the Superior way. I used it when I did my 9 day trip out of Grand Portage around Isle Royale. Lots of good information. There is a section on the Apostles where she gives you locations of docks, good anchorages (she's a sailor) , shoal areas, beaches and other useful information on each island. A must have for boating on Superior IMHO>
I love boating in the Apostles, my favorite place to boat right after Isle Royal. Be careful, once you experience it you might get hooked!
Here's a few of my pictures.
Outer Island Lighthouse. North shore in the background. Lake was pretty calm that day.
Here' walking up to the same light house
Here's the first trip I ever took up there with my 23' Larson. I went with a group. Parked in a transient slip in downtown Bayfield. You can see this area is super popular with the sailers and for good reason.
Presque Isle Bay, Stockton Island. Crystal clear water with a beautiful sand bottom - gorgeous! I've boated the Apostles mostly with a group but have done it solo. More fun with a group and safer.