I'm trying to get a cheap car rental from Ohare airport and discovered that if I rent off-site and take a cab from the airport to the location, my rate will drastically drop. I'm scanning some Budget rental locations around Ohare and found the rates at Addison, Downers Grove, Oak Brook & Lombard the best for me. Could anyone advise which location might be the best to rent from and the easiest/cheapest to reach by cab?
Any help here would be greatly appreciated.

Why not ride the El downtown where you can rent a car within 6 blocks of the Willis Tower? It depends which direction you are heading with the rental car. What time are you expecting to arrive at O'Hare? Check the hours of the place you decide to rent.

Those are all easy to reach by cab but maybe not cheap. It DOES depend on where you are ultimately going. There are Budgets near the lake and out west. Take your pick.

Going downtown puts you in a place where you can start out and go any direction. It is easy to take public transportation even if you are not familiar with it.

Consider going to a location where there is a flat rate for coming from O'hare. For example, Evanston is on the lake and costs a little over $30 for a cab. You can google for more info.

Try to find one that allows return to the airport drop at no extra charge. Avis is famous for charging more for this but local Hertz shops usually don't. Try CDP discount code 62455 and PCcoupon 182722 for Hertz.

Also, if you go to google.com/maps and find OHare airport on the map, you can then click "search nearby" over on the left and enter "Avis" or "Budget" or "Hertz" and see where they are /figure out which is closest to the airport.

I had good luck once renting from a hotel, but it wasn't at O' Hare. Might be worth a couple phone calls to the chain hotels in the area.