How far is People's Square from Old Town ?
Don't know the precise definition of the old town, but I'd say it was in the old town area.
It is in the Old Town, the Palace actually. It is the square that is just outside the West Gate of the Palace. www.visitsplit.com the city website, has maps. The Croatian name is Pjaca. So look for Pjaca just outside the West Gate. It is two minutes walk from the center of the Palace, the colonnaded Peristil
People's square, which we normally refer to as "piazza" is practically old town, too. The square started to develop at the beginning of the 13th century just outside the palace, to be more precise- to the west of Diocletian's palace.
So from the emperor's mausoleum ( today's cathedral) to People's square is one minute walk.
Hope I helped,
Thanks for your help much appreciated