Around a 2km walk from pl Rynok, visiting the High Castle (Vysoky Zamok) on Castle Hill (Zamkova Hora) is a quintessential Lviv experience. There’s little evidence of the 14th-century ruined stone fort that was Lviv’s birthplace, but the summit mound sporting a mammoth Ukrainian flag thwacking in the wind offers 360-degree views of the city and the wooded hills between which it nestles.
To reach Vysoky Zamok on foot head up vul Kryvonosa from Vul Pidvalna until you reach a cafe and toilets where you should take a left. After a few minutes you will see a set of metal steps on the right. If you're feeling lazy, you can take a taxi most of the way up, approaching from the east via vul Vysoky Zamok.