There is a web page at fightingillini.com that lists the players and who they will be playing for. A bonus: the page includes links to the teams and leagues so you can check in and see how they are doing.
As usual, the Northwoods League is big with the Illini. They claim seven of the Illinois players, including Big Ten Player of the Year Lars Davis who is playing waaayy north with the Duluth Huskies.
In the Coastal Plain League, the Fayettevile Swampdogs, another popular venue, draws three alas without Shawn Roof this year.
Finally, closer to home, the Chicago Suburban Baseball League, have four Illini. That one is close enough to maybe catch a game or two this summer.
If college summer baseball is your thing, you might want to check out Summer Ball, a web site dedicated to College Summer Leagues.
Good luck to the Illini this summer!