The Minneapolis metro area is home to a ton of great antique stores. Many in Stillwater and Hopkins sell a good selection of Victorian and French Provencal furniture and decor, and the shabby chic and refurbished trends are easy to find in Anoka, Mound and other outlying suburbs. Mid-century furniture is often mixed into the selection at those stores, but Retro Wanderlust in Hopkins is a real gem for the Mid-century furniture hunter.
The store has a good mix of decor and large furniture pieces, though digging is often necessary. They are quickly outgrowing a 3,000 square foot warehouse space, so you'll find night stands stacked on dressers piled in front of headboards and art pieces. Make sure to give yourself plenty of time to dig, and if there's something you want to get a good look at the staff will move pieces for you.
Keep in mind, like most furniture built before 1980, this stuff is usually made of solid wood (sometimes the wood is covered with laminate depending on the piece) and you can expect to pay for the quality. Prices range depending on the quality, rarity and size of the piece. I fell in love with two five-drawer walnut dressers, and they were listed at $160 each.
A few non Mid-century odds and ends are mixed in, like the pink tufted headboard in the photo below, so it's worth a trip even if you're not an Eames fan.