If you are entertaining and going to the race you might want to consider a limo as your way to get into and out of the track with the least amount of headaches.
If you drive I would also advise parking west of the track and like the "Coke Lot" which is parking on grounds around a Coca Cola bottling site. If you drive you will crawl in traffic getting to wherever you park unless you are near the Speedway before 9 AM local time (it is EDT this year which means that we are an hour ahead of Chicago.)
The duration of the race is dependant on weather and incidents on the track, but a typical race runs from 3 to 3 and a half hours. Again if you are driving your own car after the race count on traffic being slow until you are out of Indy.
Hotels downtown are probably all gone and the airport or possibly something North is most likely you best bet. If you want tour packages (hotel plus transportation to and from the track plus other extras) you may want to go to this website: www.gptours.com/new/race.php/id/6054/Indy-500
(None of these give a 2 night package for the nights you mentioned.)
As to evenings it depends on what you want as far as entertainment goes. If you want you may still be able to go to the 500 festival ball the night before the race downtown. KC & The Sunshine Band will be the entertainment this year. It costs $250 per person and for more info call (317) 614-6400 or look up more at the following website: www.500festival.com/news/index.asp?news_id=49
Have a great time and enjoy the city!