When would you be having the baby shower? Spring?
I can only think of a couple of places I think would work;
Calhoun's on the River has an upstairs banquet space that you can rent out or a seperate area on the mail level for smaller parties. That area is pretty nice because it overlooks the river and is surrounded by glass. I believe you pay for the upstairs space to rent that out but the downstairs one is just for reservations so that would be free. Their food is amazing and is great for out-of-towners that want to get a sense of good Tennessee barbeque!
Copper Cellar restaurant on UT Campus is also a nice restaurant that has seperate areas you can reserve for party events. They have great food and it is located in the heart of Knoxville.
There are several outside places I would recommend, but the weather is so unpredictable here at the end of March. I would plan something indoors just to be safe.
Hope this helps a little!