Seven Mile Beach is a public beach, and there are access areas located along the street. The hotel amenities are not public though. I did the ship excursion the first time because it included transportation and a lounge chair. The next time I just asked the taxi driver about a hotel that allows access. I can't recall the name of the one she took us to though. They did charge us for using the chairs.
Another option may be Sea Grape Beach. I haven't tried it, but have heard they offer rentals of chairs etc., and have a bar and grill.