Eglin is very forthcoming with UAS operational restrictions, since they are a DOD classified facility. I have attached a document from Eglin AFB about UAS restrictions. As you will see, there is nothing from them preventing you from flying over the beach areas east of the base.
This does not mean that local restrictions are not limiting UAS operations. It also does not include Tyndall AFB in the Memo.
I would say that you are okay to fly there, just remember that banner pilots are in the 500'-1000' altitude, and fly regularly, so adhere strictly to the 400' limit.
Camp Helen SP is just west of there, and ALL Florida state parks are off limits, so don't fly there.