I live in Indy, but mainly fish local ponds due to time restrictions. However, there are sections of the White River that are good for small mouth. Access to them can be a pain if you don't have a boat or knowledge of where to park. I would also give Wild Cat Creek Outfitters
a call. They are in Zionsville, north west of Indy and offer guided trips.
There is a section of Eagle Creek in Zionsville that's supposedly good for wading, smallies and carp. I've never tried it, but plan to this summer.
There's also Eagle Creek Reservoir, west of the city. You would be bank fishing there, unless you had access to a boat. I haven't fished there in a while, so I can't comment if it's good or not.
Brookville Tailwaters is in the south east section of the state (near Cinci), that is stocked with trout. May be a bit of a drive for you though (1.5 - 2 hours).
I guess it depends on what type of fishing (river, lake, wading, floating, etc.) you want to do. Oh, just so you know, I would not keep anything to eat from the waters in IN. I don't know if you knew that or not, but just throwing it out there.
If you have any other questions (restaurants, etc.), pm me, and I will do my best to answer.
Good luck, and have fun in the Hoosier State.