There are numerous excellent restaurants in the area - nearly all independently owned and operated.  Check days and hours of operations, as they often change seasonally.

On or very near Butternut Lake:  Northern Pines, Bobber's on the Lake, MT Pockets, Sieg's Inn and Outhouse Bar

Butternut:  Butternut Ice Cream & Treats, Double D's Pub & Pizza, Butternut Cafe 

Park Falls:   The Lanes,  Jack's Corner Bar, Vichy's Pub, Espresso Ala Mode, Park Falls Family Restaurant, Subway, McDonalds