The origins of Junii go back at least as far as the 18th century, though the modern Junii celebrations in fact date from the end of the 19th century, when the various groups of Junii (Junii meaning, literally, young men) were formed. The celebration is mix of both Pagan spring and Christian Easter rituals.
The parade begins at 10:00 in Piata Unrii, in Scheii (which in the past stood outside the walls of Brasov), and makes its way into Brasov along Strada Gheorghe Baratiu and Strada Muresenilor, before turning right and heading back out of the city along Strada Nicolae Balcescu, exiting the city through Poarta Scheii.
The parade then carries on to Solomon's Rocks (Pietrele lui Solomon) where the biggest party of the year is held until late in the evening: expect traditional dancing, music, food and drink.
The best place to see the parade is Strada Muresenilor, but note that the whole city turns out to watch: get up early if you want to get a good viewing spot.