Yes next to the Royal in council car park but make sure you purchase ticket for overnight and then in the morning if leaving car after certain time. I think you need a ticket after 9:00am but it is cheap.
Directly next to the hotel
Yes there is a pay parking lot next to the front entrance of the hotel. But is shared by "beach goers". So some times during the days spots are hard to find
Yes there is a carpark next to the hotel but not owned by them its council owned and pay and display hopevgjis helps
Unfortunately there is no free parking. There is a small council parking right next door to the Royal Hotel which you have to pay for. Hope this Helps.
Get an answer from The Royal Hotel staff and past guests.