Going to Sun City with your own agent is a good idea. It doesn't cost you a cent more than going without one, and if you tour the first time without one, you can't change your mind and use an agent later.
Sure, Del Webb/Pulte has agents on staff to sell you a house. They are
Seller's Agents. Your own agent would be a
Buyer's Agent, who would look after your interests.
Many people who purchase Sun City homes don't use a Buyer's Agent.
As for the "day pass" issue, if Sun City Hilton Head is anything like Anthem, I don't know why you'd even want to leave and go somewhere else for your recreation. There should be plenty of amenities and activities on site. That's the whole idea of Sun City