If you're short on time, have a wander around the attractive Old Town, or Verkhni Horad (Upper City). This was once the city's thriving Jewish quarter, and while most of it was destroyed in the war, a smattering of pre-war buildings along vul Internatsyanalnaya and a rebuilt ratusha (town hall) on pl Svabody emit a whiff of history.
Many of the most bombastic buildings from the Soviet and Lukashenko eras lie well outside the centre. The most jaw-dropping specimens are northeast of the centre along pr Nezalezhnastsi and out toward Minsk Arena on pr Peramozhtsaŭ (take the #1 bus from pl Svabody). A good way to see a bunch of these is to take a City Tour bus tour.