From your post it seems to me that you are expecting to find attractions to entertain you for a week in an urban area. If so, you are in for a disappointment; other than in the immediate vicinity of Cincinnati, Louisville, and Evansville southern Indiana is rural and poor.
In French Lick there is nothing at present other than the Indiana Railway Museum; the French Lick Springs Resort has been closed all year for refurbishment, along with the spa, swimming pools, tennis courts, golf courses, and riding stable. Everything is scheduled to reopen in December when the new casino and conference cents opens.
West Baden Springs has tours of the West Baden Hotel, although it too is undergoing refurbishment and is expected to reopen next summer as a hotel for the first time in many years.
There is the Holiday World Theme Park at Santa Claus, Indiana; the Six Flags Kentucky Kingdom at Louisville, Kentucky; tours of the Louisville Slugger factory near Louisville; and several show caves in southern Indiana. There is also an area that is predominately Amish and Mennonite around Montgomery, Indiana, northwest of French Lick.
I strongly recommend the tours that the resort has put together; Norris is very knowledgeable about the area, his presentations are excellent, and he will be showing you places that you never would have dreamed could be there.
I will also recommend the following restaurants:
The Overlook Restaurant can be found on Indiana Route 62 at the western edge of Leavenworth, Indiana, a small town with a population of just over 300 about 35 miles from French Lick. The restaurant is located on top of a bluff overlooking a horseshoe bend in the Ohio River, and has a fantastic view. The dining room is tiered so that those seated at tables in the interior can see over those seated near the floor-to-ceiling windows facing the river. Their specialty is fried chicken.
The Schnitzelbank Restaurant is located at 393 Third Ave, Jasper, Indiana, about 25 miles from French Lick. This restaurant specializes in authentic German dishes, but there is also a good selection of American dishes on the menu. They also have a good selection of German beers. One of the features of the Schnitzelbank is their glockenspiel, housed in a clock tower. To fully experience the glockenspiel you need to be outside the restaurant where you can see the clock tower. I believe it plays on the hour and half-hour.
The Gasthof Amish Restaurant is located 1 mile north of US Route 50, Montgomery, Indiana, about 30 miles from French Lick. Just look for the large "Gasthoff Amish Village" sign on US 50. They have daily specials and a large buffet.
In French Lick itself I like Jody's 19th Hole Restaurant and Lounge, 452 Maple Street, a local bar that also serves food, and T'Berry's Cafe, 8271 West College Street, a local cafe; I have never tried the Beechwood Inn.
There is quite a bit to do in the area, but you will have to do some research to find the things that you are interested in.