Lots of good suggestions have been posted. We've been down 6 times for a week each. On a couple of our first visits, after a busy day, we took the cart over to the area off the bridge, above Lake Sumter, on Morse Blvd. and watched the sunset. It was the most relaxing experience. I had my arm around my wife and we discussed some of the events of the day and what we liked or wanted to check out more. It was both romantic and helps you unwind from a busy day and make plans for the next day.
The second suggestion is to visit the little ponds across from the Savannah Center. There are on the entrance to Glenview. They are tiered with a little water fall. We went around 5pm and just set there in the cart parking area enjoying the beautiful ponds, flowers and birds. This is a favorite area many folks bring their grandkids and some bread to feed the fish. We met two of the most delightful gentlemen who rode up with their dogs in the cart. We struck up conversations and asked lots of questions. Two hours later, we decided we better get something to eat.
As suggested, if it is your wife you want to "sell" on TV, then let her decide on some things she'd like to do. Don't be a "cruise director" and plan her every minute. Take her on a scenic cart ride through the moss covered magnificant oak trees along Buena Vista and Stillwaters Dr. There are some park benches there under the trees and just a beautiful setting. Make a lot of time to just relax and absorb the beauty throughout TV. She will be sold!! We sure were.
Don't forget to take in a polo match while you are there too.
Best of luck!