If you are looking to see the July 3rd fireworks in a little bit less crowded environment, you can try the lawn above DuSable Harbor. This is the area north of where Randolph St. ends at the lake. The fireworks are launched to the south so you will be viewing them over the boats docked in the harbor.
From the Fairmont, go to the river walk then walk east to the lake, then south just a bit. There will be people on the lawn by the harbor, but nowhere near the mob scene 3 blocks south of there.
If you will be there drop me a PM and I'll tell you which boat pier I will be on.