The snow better be gone by May. If you're going to be by Naperville I can recommend both the West Branch of the DuPage River and the Fox River. Both are good rivers for smallmouth bass and the DuPage has a nice population of rock bass and a few good size bluegills too.
The DuPage flows right through Naperville and oddly enough some of the best fishing is right in town. Most of the river flows through parks or forest preserves so access isn't an issue. The DuPage is a small shallow rocky stream that lends itself well to wading.
If you go farther to the west towards North Aurora you'll come across the Fox River which is much wider than the DuPage but is also shallow and rocky. There is also a chance of picking up a bonus walleye in the Fox. The Fox flows through several towns (St.Charles, Geneva, Batavia etc.). These are all older communities (former mill towns) with old dams and also with some very nice restaurants and antique shops. One area on the Fox I can recommend is fishing below the lower Batavia Dam. Dam is kind of a misnomer as the dam is a low head dam (as are all the dams, not like the TVA or Corps dams). This stretch runs through a forest preserve and you'll fell like you're in a remote area. You'll see plenty of ducks, egrets, herons, deer and and even a bald eagle sometimes. The usual smallmouth patterns work fine.
Given this cold winter the bluegill and crappie spawn will definitely be delayed. You might be able to hit the spawn. You can try Silver Lake in the Blackwell Forest Preserve.
For more info on DuPage County Forest Preserve lakes go to;