As others have posted, take the trolley tour from the sales office at either Lake Sumter Landing or Brownwood. It takes just under an hour, and it is narrated by a guide who lives in The Villages, so you can ask questions during the tour. Yes, go to as many country club restaurants as time permits. If you go on the restaurant section of TOtV, there are reviews on just about every restaurant in and around The Villages. I have eaten at most of the country club restaurants during my visits to The Villages, and there was only one cc restaurant that I would not go back to.
And there are open houses held every day in The Villages for both new and pre-owned homes. You may want to go to a few of them if you have time, just to see what is out there. If you grab the Daily Sun newspaper, the open houses are listed there (both through the MLS real estate agents and The Villages real estate agents). The Villages web site also lists the open houses daily.
If you get lost in the golf cart, no worries. If you pull off to the side of the path with a map, chances are a helpful village resident will soon drive by and stop to see if you need directions. If you meet people on the squares or in restaurants, don't hesitate to ask question about their experiences living in TV. Most villagers are happy to answer questions.
Have a great time during your visit to TV.
P.S. I have stayed at the Towne Place Suites in TV -- good choice. You are right in Spanish Springs next to the movie theatre. Restaurant recommendation -- eat breakfast at Athens Restaurant in Spanish Springs -- mmmm good.