We were fortunate enough to stay in a 2 bedroom at HHI a few years ago and LOVED it!! We spent plenty of time on the balcony and in the hammocks that were just outside our room.
I specifically recall a picnic table with bench seating on the balcony and not much else -- I seem to remember having to bring chairs from the inside to have something to sit on that we could position where we wanted it as opposed to being attached to a table. We also ended up buying some of those collapsable chairs that you can find everywhere now, the ones that fold into a tube, to take to the beach and we ended up using them on the balcony, too.
I will look through my pictures and see what I can find for you.
If they have changed in the past year or two I am sure someone will be able to correct me.
You are going to have a FABULOUS time!!
Edited: Just checked a few pictures -- there were 2 wooden rocking chairs on the balcony, too!!