I have just added this to the map of places to fly your drone at Drone Scene:
Land owner permission requirements unknown.
Plenty of car parking available at various places around this park. It's home to Bangor Castle (Town Hall), North Down Museum and The Walled Garden. Entry is free and there are cafes and toilets. Worth visiting all year round but even better in Autumn for the colourful trees.
The originator declared that this location was not inside a Flight Restriction Zone at the time of being flown on 16/09/2021. It remains the responsibility of any pilot to check for any changes before flying at the same location.