If you're entering Belarus from northern Poland, or if you have extra time in the country, think about visiting Hrodna (Grodno in Russian). It was one of the few Belarusian cities that wasn't bombed during WWII, so it's rife with old wooden homes and, although it's a major city, it definitely has a 'big village' sort of feel to it.
The historic city of Vitsebsk (known universally outside Belarus by its Russian name, Vitebsk) lies a short distance from the Russian border and almost 300km from Minsk. Vitsebsk was an important centre of Jewish culture when it was one of the major cities of the 'Pale of Settlement', where Jews were allowed to live in the Russian Empire.
Leave Minsk for an easy taste of the gently appealing Belarusian countryside, a world where instead of mobile-phone shops and sushi bars, the few stores you'll see will have names like 'Bread' and 'Shoes', dating from a bygone era of no choice. Don't miss the fairy-tale castle at Mir or the beautifully restored palace at Nyasvizh.
The magical old buildings of Nyasvizh make it a great place to get in touch with Belarus' past – one that elsewhere has all too often been destroyed as the military campaigns of WWII flattened the country. This quiet but green and attractive town 120km southwest of Minsk is one of the oldest in the country, dating from the 13th century.