Cab can be much slower than EL if it's rush hour that you are arriving. Cost won't be much different than the standard $40, maybe $5 more unless you are stopped dead on the freeway due to some major accidents, etc.

You should get off at Clark&Lake stop if taking the EL Blue line from ORD, and then hop on a Cab to drake, which should add about $5 (tip included) to the $1.75 EL cost.

If you are really cost conscious (doesn't sound like that you are), you can get off at Washington (the stop right after Clark&Lake stop) and transfer (free) to Red Line north, and get off at Chicago (just two stops after the transfer), and then walk to Drake (5 minutes walk unless u have a boatload of luggage), all for $1.75.

More detailed EL map for the downtown (a.k.a. Loop) area:
http://www.transitchicago.com/maps/maps/F2004D.html