All posts have given you good advice. My suggestions are in no particular order are:
1. Take the trolley tour.
2. Visit the squares for dancing, (just show up).
3. See the Eisenhower Rec Center, as it is impressive.
4. Talk to anyone and everyone.
5. Don't stress yourself by trying to see everything in 4 days but relax and enjoy your visit.
6. There is no bad section to buy a house in.
7. Look-up other posts on new vs pre-owned.
8. There will be no pressure from sales people, as The Villages beauty sells itself.
This place is immaculate.
9. Most of all, enjoy yourselves. You are in for a treat.
BTW - Bring your checkbook.
__________________
"It doesn't cost "nuttin", to be nice". 
MOM
I just want to do the right thing! Uncle Joe, (my hero).