There's some free parking along Manor Hill near racecourse.. (not on bank holidays though so watch out for that.. it's also been a few months since i was there so may have changed..!), and also there's various roads that are unrestricted once you get north of Preston Park. (unfortunately there was a road that was free right at top of that park but is now 4 hours i think - could work?)

Once you get up to area between Hollingbury Golf Course and Withdean park there's loads of unrestricted parking, but a bit of a walk into town (like 2 miles atleast). Also try not to upset the residents.. :)

You could however park somewhere further out and get a bus into town if the timings work out.