I agree about staying at the Waterfront Inn. The rooms, bedding, lake views, and walking distance to Lake Sumter Landing town square and live bands/dancing are superb at excellent prices.
I checked the website for Sunday night, and a double queen or king room with lake view is only $139. Here's their website:
Waterfront Inn Villages | The Villages, FL – USA
The other suggestions are good too, about the trolley tour which allows you to see the whole community with guides explaining it all.
And, talk with people sitting at the patio bar-restaurants and at the town squares where people are dancing to live music every night of the year. There's no place like this!