This app was mentioned in 1 comment, with an average of 2.00 upvotes
I can help you with that. Coresi and other shopping centres usually have their own free parking, but other parking spots, especially in or near the old town, have a cost of 1.5 Lei (£0.3) per hour. However, they are free from 8:00 PM to 8:00 AM and on Sundays.
You can pay with coins at these things or install this app, though I'm not sure how well it works for non-romanian numbers.
Edit: Damn, too slow!