Round lake is extremely clear according to the limited info I have. The info says that it is the 10nth clearest lake in all of Illinois (who knows how the hell they test that ).
The lake it self is shallow around the edge with two basins in the middle. There is a shallow part in the middle between the two basins which I would try if I were you. Weed beds in the shallow areas should produce some bass also. Below is a link to a decent depth map. http://www.co.lake.il.us/health/pdfs/ehs/maps/round.pdf
They used to stock the lake with bass and walleye in the early 90's. There a good bass and bluegill population but I doubt you'll see any action from the eyes. I read that every once in a while you'll catch a nice pike there.