Radsmom,
While P42 is right, there are indeed lockers in the station; there is no need for you to use them. Since you are in a sleeper, you can take advantage of a special locked room for sleeping car passengers. A redcap attends this room during the day. At night when you go to leave it will be locked, you'll however be sitting in the Metropolitan Lounge by that time.
When they make the first call for those needing redcap assistance, you will go up to the front of the lounge. The redcap their will help you to retrieve you luggage from the room. You can then either return on your own to the lounge with your luggage and board with the rest of the passengers, or you can stay with the redcap and have him help you out to the train. Of course then you will have to tip him.
You can find this special room by heading through the sliding glass doors that lead to the Amtrak Information desk (not the ticket windows), and the Amtrak waiting rooms. Once through the double doors, 10 paces or so will bring you to a north/south hall. (Note: The Metropolitan Lounge is slightly to your left and straight ahead through another set of sliding doors.) Turn right towards the south waiting area. Another 10 paces will bring you to the end of that hall where you will turn right again. You will find yourself standing in front of the luggage room.
Simply give your bags that you are carrying to the redcap and show him your sleeper tickets. Tell him that you are leaving on train #40. He will put a #40 sticker on your bags and give you claim checks for the bags. There is no charge to use this room; it's free to all sleeping car passengers.
Then you can go off to wander the city. Note, this is only for your carry-on bags. Any luggage that you checked at LA for Orlando you don't have to worry about at all. Amtrak will handle that separately.
By the way, there is also a storage room within the lounge. However I don't recomend using this room since it is not attended. Passengers simply place and retrieve their bags in that room. I prefer the secure room where your bags are actually checked by a redcap.
Now Sears Tower is a two-block walk from the station. You want to walk east on Jackson Avenue. Jackson is on the south side of the station. When you come upstairs if you don't immediately see the Chicago River, then you are on the west side of the station. It should be noted that the Sears Tower isn't cheap. They also will search all bags and then make you view a safety presentation, before you ever get to go upstairs.
There are also many other things to do downtown too. One can lunch in the many food places and restaurants. A nine-block walk will bring you to a very large park located right on the shore of Lake Michigan.
This map from the Chicago Transit Authority will help to give you the lay of the land in the area of the station.
Finally, I can't remember since I've given them out so many times, but did I tell you where to find the Club Acela Lounges in Philly and DC?
