If you are looking for overnight accommodation on race weekend, then you may wish to consider the following:

Indianapolis International Airport is situated just outside the city of Indianapolis. Getting into the city is about a 15-20 minute ride by bus or taxi. Visitors from Europe may find it easier to fly into Chicago and travel down to Indianapolis by road or train.
The circuit is situated on the edge Indianapolis so this is the most convenient place to stay. The city has a range of accommodation available, but book early to secure accommodation to suit your budget.

Camping is available adjacent to the circuit but this should be pre-booked.

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The interactive map below shows the location of Indianapolis Motor Speedway. Use the controls to view the circuit as a traditional map or as satellite images, move around, and zoom in and out.