assuming you are coming over via SR-528 aka the 'Beachline'
the easiest park - and in the opinion of many the best - is Jetty Park
https://www.portcanaveral.com/Recreation/Jetty-Park-Beach-Pier
when 528 end at the port just follow the signs .... at the south side of the port enterance is Jetty Park. You will find a beach with life guards, concessions, rentals showers and facilities. There is a per vehicle charge to enter. Depending on the day of the week this is also a great place to watch cruise ships depart . . .
This is a popular family beach for the area. Others have mentioned 'the pier' which tends to have a young and surfer crowd.
If you want QUIET BEACH ... pickup I-95 south and go to exit 188, the Pineda Causeway and take this to the beach .... about 7 miles east. here you'll find the beaches around Patrick AFB which ARE publicly accessible and WAY less crowded .... with FREE parking ...
most entrance points have simple restrooms and outside shower. Often when I go to the beach here (near my house) I can look left and right and see fewer than a dozen folks on the beach ..... bring your drinks and snacks and blankets ... no services here. It is PLAIN BEACH ... FOUR MILES of plain beach ....
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OR, do you want to SEE the ocean without getting sand in your toes?
This too is possible. I recommend either going to the pier as others have mentioned. Not for the beach but for the places ON the pier ....
http://www.cocoabeachpier.com/
OR Coconuts on the Beach ....
https://www.coconutsonthebeach.com/