Anywhere you have lawful access to the water. The only exceptions are a handful of parks that have ordinances that prohibit scuba diving and possibly a few places where swimming isn't permitted. (Whether these ordinances have the force of law is highly doubtful in most cases, because of state preemption, but that's not what you're here for, so I'll save that for another time)
The main problem is finding a place that's interesting to dive. Common dive sites include:
Lac Lavon
Square Lake
Perch Lake (Wisconsin)
Lake Ore-be-gone
The many mine pits in the Brainerd Lakes area
Lake Superior
Lake Minnetonka is a favorite for ice diving, because there are cool wrecks to see but the viz and boat traffic make for poor quality dives in the summer.
Lake Wazee, in Wisconsin, is also a popular destination.
There are many others.
What part of Minnesota are you in?