If you stay at the Backcountry Lodge or Kantishna Roadhouse, they have activities for you there and near Wonder Lake. But they don't have permission to drive their vehicles back into the park past Wonder Lake. You can buy a separate bus ticket to get you into the "heart" of the park as I call it to go hiking, etc. But then you are defeating the purpose of spending all that $$ at the lodge and missing out on their activities (which except for Camp Denali and North Face Lodge, are not worth what they charge IMHO).
If you are coming from Chicago then yes you would need to change planes in Anchorage. Probably arriving in Anchorage non-stop might be best. That does give you more options to explore on the way to/from Denali. If you are interested in hiking on a glacier, the Matanuska Glacier is not a long detour from the road between Anchorage and Denali (a good hour plus each way). You can take a 2 or 3 hour guided hike on the glacier for +-$100. Gardyloo gave you some other options above.