The Eiteljorg Museum, the Indiana State Museum, White River State Park and the Zoo are all close to downtown.
I have heard great things about the "Mass Ave" area downtown, for shopping, dining, etc. but have not yet been down there.
Although it is a few miles from downtown, if she likes shopping, she might enjoy the Broad Ripple area too.
The Children's Museum is downtown and is pretty great, but maybe not so much if you don't have a child with you!
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If ignorance is bliss, there ought to be more happy people.