A few options up there...
#1 Aitkin MN-KAIT FLY-IN on 6-26!!!
Great little airport to stop in to, especially on the weekends. The people there are great. Pretty much will not let you leave until you have something to eat from the fridge.
B.Y.O.M. (meat), the grills there are turned on every weekend for people to come grill, and watch planes.
I believe it is about 30 nm flight SW of DLH.
#2 Madeline Island, WI - (Don't know the identifier)
It is straight east of DLH, again about 25-20 nm
#3 Cloquet (KCOQ)
You're in luck! The fly-in is this weekend (6-25/26) Only about 15 S of DLH!
http://www.dot.state.mn.us/aero/avoffice/events/fly-ins.html
As far as BBQ...you're in MN; not TN. Walleye is king up here. "Grandma's" in dtwn DLH is good spot, but "touristie". Right on the Harbor too, lots of boats and ships there. Also, many other options for food/fun on the boardwalk right there too.
Ask the guys at NorthCountry, they will help you out.
Lemme know how it goes.