Bruin, here are a few things I'd suggest that haven't been mentioned yet:
Bottleworks just northeast of downtown on Mass Ave is a cool revamped area repurposing the Coke bottling factory. There's one place there called the Garage that has a dozen or more food options. There are other cool bar and restaurant options up that area, too. Good place to walk around.
Depending on age of your son, the Indianapolis Children's Museum is the largest in the nation. Lots of good exhibits and stuff to do.
If he's a bit older and y'all are into history the Indiana State Museum is a good place, plus you can get your parking validated when you go in the museum and only pay $4 to park in downtown. Indianapolis has the most war memorials of any city in the nation other than DC. The best one is the Indiana War Memorial & Museum just north of downtown. Amazing history and a collection you could take hours exploring; it's also a really cool building. I'd prioritize the War Memorial over the State Museum.
Hotels - other than the previously mentioned JW, my favorite hotels in downtown are Bottleworks Hotel and also the Alexander.
Not to discredit St Elmo's but there are a good number of downtown restaurants that are significantly better than StE. If y'all have never had the shrimp cocktail, go to StE's partner restaurant next door - Harry & Izzy's , sit at the bar and order a couple drinks and the shrimp.
Bluebeard - $1 oysters on Sundays.
Livery - my favorite place
Favorite dishes: Tuna tostada, watermelon aguachile salad, skirt steak.
Beholder
Vida
Milktooth
If you want a good breaded pork tenderloin sandwich, go 15 mins north of downtown, there are two in Broad Ripple:
The Pawn Shop - a true dive bar, loin is only $7. My favorite tenderloin in the city.
Plump's Last Shot - lots of old basketball memoribilia on the walls, a cool history of high school and college basketball in the Hoosier state.
There is no good Italian place in town, but we do have some really good pizza, surprisingly. On Mass Ave there is Goodfellas (NY style). Portnoy gave it an 8.2 in his review. Just outside downtown is Sam's Square Pie that does Detroit style and is absolutely fantastic. Futuro, also just outside downtown offers both Detroit style and Chicago tavern style. Get the tavern style there and the Detroit at Sam's.
If you have the coin to pop on the Indy Car ridealong experience... there really is nothing else like it. I've gotten to do the Nascar experience at Texas Motor Speedway and drive the car, and it doesn't hold a candle to going 200mph flat out at Indy, even if you are just the passenger in a 2-seater. The museum was recently completely redone (its in the infield) and it is pretty awesome.
Let me know if you have any other specific questions or want any other recs.