It's been a while since I stayed in this area at the holiday inn express. Their free shuttle service took me to a little beach across the road that had restaurant/bar on the water. Would your shuttle take us there? And, they took us to a mall nearby?
Yes, Chase Suite Hotel can shuttle you to Ben T Davis beach, Whiskey Joe Bar,West shore Mall, International Mall,(5 miles radius) need to schedule shuttle in advance at the front desk.
Get an answer from Chase Suite Hotel- Tampa staff and past guests.