If you look at this map for the pedway: http://www.spiegl.org/pedway/pedway.html

you will see the Clark and Lake stop is very close to the State of Illinois entrance. If you are only rolling one manageable bag and you are a walker then I would say you could use the pedway to get you to the Radison. You can exit at the Fairmont and walk across the street to the Radison or keep going to the Aqua. You will see doors that lead to the Radison elevators. Otherwise, get a cab when you exit the subway. Then you can take your time and explore the pedway without the luggage burden.

We had a very nice meal at the Filini and would gladly return. Look at the menu and see if you like it.