Parking in central Varna is difficult its true but thee are quite a few pay car parks for those willing to pay.
CHERNO MORE HOTEL< ODESSOS < BACK OF LONDON HOTEL(FORMERLY MASALA PALACE, TRAIN STATION etc
But heres a tip.....
ALL the Mall car parks are free as are KAUFLANDS & CARREFOR car parks.
Parking away from the centre and using your legs for 10 minutes works quite well too
I live in the centre and I always find a space.....Not always near my place but within walking distance....
......Try doing it in Central London..