Duluth typically has ample apartment availability. If you give yourself between 45 and 60 days to find a place, you shouldn't have any problem on your apartment hunt. If you look in the summer when availability is up, you will probably need even less time than that.
Duluth is one of those cities that often has a lot of rental apartments advertised in means other than on the Internet. You can find plenty of listings posted at the University, for example. A drive around some of your preferred neighborhoods may also yield some "for rent" signs that are posted right in the windows of available suites.
There is a small public transportation service in Duluth that the Duluth Transit Authority provides. These routes are limited though, and driving is more practical solution. If you haven't done a lot of winter driving, prepare yourself with winter tires for the snowy season.
If you wan the best view of the entire city, head to the top of Enger Tower. Leif Erickson Park celebrates the Scandinavian heritage of Minnesota. The most "tourist" friendly district is found at Canal Park, but the dining and shopping are certainly also popular with the locals. Spirit Mountain is a nearby Ski Resort that gets quite busy in the winter. For a local bar that brews their own beer, check out Fitger's Brewhouse.