There isn't a whole lot unless you go to Louisville...

You are about 30 miles (west?) of historic New Harmony, Indiana. We've stayed at the quaint New Harmony Inn (some rooms have fireplaces). The Red Geranium is a gourmet restaurant in the premises. http://www.newharmonyinn.com/
It's a peaceful town where you can spend several hours just walking around the small town with its quaint shops, antique stores, etc.

A bit further out, about 90 miles NE of Evansville (about a 2 hr. drive): West Baden Springs Hotel in West Baden, IN, has been beautifully restored and in 2009 was recognized by AAA as one of the top 10 U.S. historic hotels. It was listed on the National Register of Historic Places in 1974, became a National Historic Landmark in 1987 and is a Historic Civil Engineering Landmark. The hotel has a 200 ft. domed atrium and has been dubbed as the 8th wonder of the world.
See the reviews: http://tinyurl.com/y9phhp2

Also, check out French Lick Springs Hotel practically next door. There's quite a bit to do: shopping, golf, spa, riding stables, casino, etc.

The ff. website will give you more info on both hotels:
http://www.frenchlick.com/hotels/index.jsp

Mammoth Cave in Kentucky is about 2.5 hrs. SW of Evansville. If you want to try some spelunking, this is the place to be, with cave tours ranging from child-friendly/elderly-friendly tours to the Wild Cave Tour. Note the description for the latter: "lengthy crawls through areas as tight as 9 inches high; walking in a crouched position; hand and knee crawls over jagged rocks and dirt; crawling through wet areas; twisting into and out of tight crawlway openings". Fun, huh? The Wild Cave tour requires you to wear "High-top, over-the-ankle lace-up boots, with lug or deeply treaded soles". Also, your chest measurement may not exceed 42 inches. I kid you not.

For more information about Mammoth Cave, here's the website:
http://www.nps.gov/maca/index.htm
Note that reservations are required for the cave tours.

A few of the non-chain restaurants that we have enjoyed in Evansville:
Taj Mahal, Thai Papaya Cuisine, Vietnamese Cuisine (that's the name of the restaurant), Yen Ching (Chinese), and for fine dining: House of Como (really good steaks), Edgewater Grille (right on the Ohio river), Acropolis (Greek), and Raffi's (Mediterranean).

As the other poster noted, Louisville is a good place to visit, about a 2 hr. drive. You'll see the Louisville Slugger Museum and Factory, and while the Kentucky Derby Museum is closed because of flood damage, you can tour Churchill Downs. http://www.derbymuseum.org/

Nashville, TN is about 2 hours away, St. Louis, MO about 3 hours away.

It all depends on how much time you have in Evansville.

Thank you both for your valuable inputs. I get a good feel of the area already.

best regards
Raj