could someone tell me if I can get there easily with public transportation on a sunday morning or is a cab the best way to go....I know nothing about chicago public transit...thanks

A cab is definitely the best way.

A cab is going to cost you around $35 from O'Hare. Public transportion is so easy (unless you have loads of luggage)
Take the Blue line train (the EL)for $1.50. Just follow the signs at the airport for the trains to downtown. You will probably want to get off at the Washington stop. From there you can take a $5 cab ride to the hotel, jump on the Red line (EL) going north and get off at the Grand stop (two blocks from the hotel) or catch the 151 or 157 bus on State street (which is one block to the east of the Washington exit). You can pick up CTA (Chicago Transit Authority) maps at the airport.

you could always take a shuttle to your hotel if its too much hasle with your luggage on the EL, details below

http://www.ohare.com/ohare/ground_tr..._shuttles.shtm

thanks to everyone...I will play it by ear when I arrive. Mary, thanks for all your directions. Timewise will the Blue El be as time efficient as a cab on a Sunday late morning? Your advice if tge el to a cab at washington seems like a great bet!
thanks for your time