Check out this website about Green Valley..
Green Valley Chamber of Commerce - Green Valley Arizona Travel and Tourism
It should list all the activities that they have in the area.
Like the previous poster said...golf is a huge thing to do. A lot of people also are huge into bike riding. There is also madera canyon close by where you can enjoy hiking and other outdoor things. Very nice area...
I do have to disagree about the comparison of temps with Tucson. Its not just a couple of degrees cooler. Its about 10-15 degrees..which is a big deal during the summer. It also rains a WHOLE lot more.(I live right on the border of Green Valley and Sahuarita so I know the difference of the weather)
If you want a small town feel, then Green Valley is a good choice.
Hospitals are about 30+ miles away..if your in poor health, that is something to consider. There is an urgent care facility opening in the area some time soon, but I don't know when.
One more thing..in Green Valley you have to watch out for those speeders on the golf carts. They'll run ya over if your not watching..lol