I didn't stay at the Hyatt so I can't help you there.
However, it's easy to hail a cab in the morning cause there are tons of them going by. I would think though, that to be safe, you might want to call a taxi service the morning of the interview so that they can come and pick you up, and you know they're coming. That's what I did in Boston and it worked well.
There are two entrances to ICO. The clinic entrance is on South Michigan avenue (the one way going south that goes by ICO, and the entrance that you'll want to be going in is 3241 S Indiana Avenue, which is the one way going north on the other side of ICO. This entrance is across from the RC. I believe that once you're on South Michigan avenue in the downtown area, you just take it until it becomes the one way, turn left on 33rd avenue, and left again on S. Indiana. The entrance that you want to go in has a very small parking lot (6 cars or so) in front of it and a bus stop. S indiana isn't usually very busy.
Hope this helps
Eyegirl.