The following parking areas are avaliable in or close to the old town center:
Pakring area in the City park
Parking area next to the Railway station
Teharska parking area (on the other side of the Railway station)
Camper parking is avaliable at the Camper stop and the City park area.
Parking spots in Celje are divided into Blue Zone (indicated by the blue line on the floor) and II. Zone.
The Blue Zone opening hours: Monday to Friday from 6:00 AM to 4:00 PM, Saturday from 6:00 AM to 10:00 AM) for the following streets: Cankarjeva ulica, Gledališka ulica, Gledališki trg, Gosposka ulica, Slomškov trg, Kocbekova ulica, Miklošičeva ulica, Ozka ulica, Kocenova ulica, Prešernova ulica, Stanetova ulica, Stara Mariborska cesta, Trg celjskih knezov, Turška mačka, Zagata, Razlagova ulica, Ipavčeva ulica, Savinjska ulica.
The Blue zone parking opening hours: Monday to Friday from 6:00 AM to 6:00 PM for Gregorčičeva ulica, ZD Celje, parkirišče Vodnikova in Ipavčeva (hospital).
II. Zone opening hours: Monday to Friday from 6:00 AM to 3:00 PM for the following streets: Aškerčeva ulica, Cankarjeva ulica – pasaža, Mestni park, Spodnji grad, Teharska cesta, Vrunčeva ulica, Železniška postaja, Oblakova ulica I in II, Oblakova ulica, Ipavčeva ulica, Jenkova ulica, Jurčičeva ulica, Kosovelova ulica, Malgajeva ulica, Trubarjeva ulica, Mariborska cesta (Faculty of Logistics).
For the complete list of parking options see here and the price list here.