Try Rustica and Breadsmith for challah (Rustica may have brioche as well). They are good versions. Lund's and Byerly's have decent versions of challah in a pinch. Turtle Bread probably has good brioche, but their challah is way too crusty for my taste. Fishman's is the best, for future reference, but they are not open today as it's Shabbat.
816 W 46th St, Minneapolis, MN 55419
3939 W 50th St, Minneapolis, MN 55424
Fishman's Delicatessen and Bakery
4100 Minnetonka Blvd, Minneapolis, MN 55416
Turtle Bread Co.
4762 Chicago Ave, Minneapolis, MN 55407