Great place, but unbearable amount of tourists... ...

Great place, but unbearable amount of tourists... the main pain point are the ferry waiting lines to get to the island and then get back. On the way in consider purchasing tickets online that allow to skip a considerable amount of waiting both for the ferry and for the visit to the statue itself. If you plan to visit the crown of the statue make sure to book months (5/6) in advance.
The island itself is very nice with awesome views, and the little statue museum is also quite enjoyable.
Make sure to pack some water and snacks (or lunch) because options are limited and expensive.
On the way back keep an eye on the ferries arriving from Manhattan to try to get to the top of the waiting line without waiting too long.
Anyway done once but probably never again... :)