Maybe the people writing the original post plan on walking to most places once they move here. The obvious choices in that case are to stay at one of the town squares.
That said, I'd recommend staying at either Spanish Springs or Lake Sumter Landing Town Squares, in one of the hotels at each (links below).
Also, long-time villagers telling a newbie to see TV via golf cart have lost all concept of how big the place is and how unusual the golf cart paths, tunnels, etc are. And when groping to find one's way, the last thing you want to do is get into a vehicular accident with a golf cart having almost none of the safety features a car has for personal protection!
Waterfront Inn at Lake Sumter Landing, The Villages:
Home - The Waterfront InnThe Waterfront Inn | The Villages, FL – USA
TownPlace Suites by Marriott at Spanish Springs, The Villages:
TownPlace Suites The Villages - Hotels in the Villages near Spanish Springs
The Lifestyle Preview Stay is a great way to stay, but I'd say
only if the villa provided is at Lake Sumter Landing and not Brownwood town square, because of Brownwood's distance south from the center of TV.
Some here have said they felt stuck in No Man's Land and having to drive far to get to the main areas of TV when doing Lifestyle Preview Stay near Brownwood.
Lifestyle Preview Stay:
The Villages - Lifestyle Preview Plan