To get down there you could easily get on the L Purple line at Wilmette/Evanston and take it to the Red Line at Howard station. From there take the Red Line to Grand station which takes you right downtown to N.Michigan Avenue area which is less than a mile from Navy Pier. From there you could Uber or bus to Soldier Field.
Costs $4 for 24 hour parking at the Purple Linden station and $5 per person for an all day L train ticket. Bus would probably cost $1 per person each way.
May sound complicated but as long as you do a little research and learn the process it really isn't that hard to get around with the public transportation in Chicago. Plus it's a lot cheaper and minimizes the headache of driving downtown.