To reach public parkings you don’t need to go through car free areas (and therefore you don’t need a permit). The closest public parkings are ‘Vrijdagmarkt’ (P1) and ‘Ramen’ (P8). See Publieke parkings in Gent.
‘Vrijdagsmarkt P1’ public parking: rate is €23,50 per 24 hours (located 200 meters from the hotel)
‘Ramen P8’ public parking: rate is €14 per 24 hours (located 650 meters from the hotel)