Frankly, your best bet (since you don't know the city) is to take a taxi. It won't be too expensive, certainly less than $20 each way (I know, that sounds like a lot, but it could be worse). For bus schedules, check
www.transitchicago.com. If you're going around the holidays, at least in past years, they've run a free trolley from the train stations to Navy Pier and State Street, but honestly, the buses can be very confusing. I've lived in Chicago, and wouldn't take the bus now unless it was my only choice.
Eating -- several of my faves have closed lately! (I was going to recommend something, but went to the website to check it out and the restaurant I wanted wasn't there anymore.) If you want to go to State Street, the Walnut Room in Macy's at State and Wabash is very nice (sit-down, and a little $$$). They MAY also still have the old Marshall Fields (that's what this store used to be) ice cream parlor, which was way cool. I tried to check on the Macy's website, but there was no info about this specific store other than hours and events. If you're interested, you could call - 312/781-1000. You can go to
www.choosechicago.com and gets lots of info. Water Tower Place on Michigan Ave. is cool, and has a food court on the bottom level. Right next to Water Tower, you can go up to the top of the John Hancock building (if the weather is nice, otherwise don't bother) and see the view from the 95th floor (costs to go up). Have fun!