I am happy to give up my seat for the following:
Pregnant
Injured (broken leg, etc)
Elderly
Other than that, I've been walking miles and miles around a park just like you and am just as tired as you, whether or not I am male or female. I'm not necessarily inclined to give up my seat. If you absolutely have to have a seat and cannot stand for 15 minutes, I would suggest waiting for the next bus or doling out the $15 or $20 to take a cab to your resort, rather than trying to guilt someone who was there before you into giving up their seat.