The above advice is all good if you are staying off-site. One option to consider is camping in the fields surrounding the track. Camp spots generally run $120 a day or so (reserve now!) and you may be able to find a rental RV, or pop-up camper you can rent through El Monte, or another RV rental company. You may want to arrive on Friday if you go this route, as all the good spots are taken by Sat. Camping is much more .....ah....festive, and you'll meet all kinds of .....umm.....interesting folks! It's a blast, but do not camp with children (besides lot 6). This is one of the world's largest parties, and they'll be exposed to things you may not be comfortable with.
Avoid the Coke lot--- Lots 1a and 1c. This is where all the college kids get wasted, burn port-o-lets and generally cause mayhem. VERY fun place to visit--- not a fun place to try to sleep.
Lot 2 is a middle ground--- plenty of partying, but not as crazy as the Coke lot-- it's also near the start-finish line for easy access inside the track.
Lot 6-- shaded, electric hookups (reserve now!) and mostly older-- quiet at night. Best place to camp, but if you are with a rowdy group, you may disturb your neighbors.
In either lot 2 or 6, you will have easy access to the track.
The track has also started offering "Glamping" sites within the track. It looks like they will have a campsite set-up in the infield---for the first time in over 20 years:
http://www.indy500snakepit.com/index.php/glamping/
We always camp in lot 2 or 6. This allows us to easily bring food + drinks into the track without breaking our backs. After the race, we don't even attempt to drive home until dusk. We relax, have a few beers, cook out, and throw the football around while everyone else is frustrated-- fighting traffic. We then smoothly leave town around 7 or 8pm. (keep in mind we are towing a 35ft trailer, so dealing with traffic isn't ideal)
This will be my 25th consecutive Indy 500 and I plan on going every year until I die. This system works well for us, but YMMV.
** Plan on being inside the track a couple of hours before the race if you want to witness all the pomp and circumstance. (Jim singing "Back Home in Indiana", Florence Henderson singing "America the Beautiful", etc.)
** The lone solider playing "taps" on the bugle before the race is one of the most moving, loneliest things you will ever hear---- it really brings home why we celebrate Memorial Day"