I live in the metro, a few miles away from the site of where Floyd was killed last summer. If I didnt watch the news I never would have known a difference. People saying avoid the area like the plague clearly dont live here themselves, you'll be more than fine in Burnsville.
My profile pic came on Mille Lacs, so I may be a bit biased, but that lake is absolutely plum full of awesome walleye + smallie fishing right now. Muskies could be a thrill there too if you found a good guide. Id much, much prefer that over any lake near the metro. If you want the true northwoods experience I'd fish on Leech but thats about twice the distance. If you want to be disappointed go ahead and stay local and fish a place like Minnetonka. Pool 4 fishing in Lake city would be neat, get to see the bluffs then, which are about as close to mountains as MN will get. Good fishing too. Charter on Superior might be cool for an out-of-towner but I've never done it myself. Duluth is a great way to spend a day with the family.
Other than that, MOA, Taylors Falls/Barn Bluff hikes, or a Twins game. Real, real tough to beat Target field on a nice summer evening. Finding a place to rent side by sides would be a great way to spend a summer day. My favorite is a little north of Hayward, Wi but that might be a bit of a hike for you guys, within about an hour or so of Duluth if you decided to make it a multiple day trip from Burnsville.