Is it possible to find any safe Lodging that is affordiable for 2 college students for the Indy 500???

You probably won't find anything for that. You can still get reservations, although they aren't the best places!(There is no need to plan 1-2 years in advance as stated above-around 4 months before is about right). You will pay 100-400/night for a hotel in Indianapolis. We usually pay around $175/night. Most places also require that you stay a minimum of 3 nights during the 500 weekend.