This map shows areas of Minneapolis that are located within 1/4 mile (bright reddish-purple shading) and 1 mile (lighter purple shading) of a freeway mainline. Due to its divisive nature and regional significance, I have included Hiawtha Ave in the analysis.
As you can see, most of the city is within a mile of a freeway mainline, with the main exceptions being sections of North Minneapolis (west of Penn Ave N), Northeast Minneapolis (mostly north of 27th and east of University), a good chunk of Southwest Minneapolis (Lake Calhoun, Lake Harriet, and Linden Hills), and small bits of south Minneapolis.
Most of the negative aspects (noise, pollution, etc) of freeway proximity happen within 1/4 mile of a given freeway. Thankfully, much less of the city is within this proximity, though it does include the entire Warehouse District and chunks of Seward and West Phillips.
Of the roughly 57.4 square miles in the city, almost 46 square miles (about 80%) are within 1 mile of a freeway, and just under 16 square miles (about 28%) are within 1/4 mile of a freeway.