Yes, there is parking at La Salle and Stockton on the south side of the park and at the Lincoln Park Zoo with the entrance at Fullerton off Lake Shore Drive. Otherwise, if you're lucky and timely, you can find parking along Stockton in the park or on streets west of the zoo.

It is fairly easy to get from the Lincoln Park neighborhood to Soldier field. You can take the Red Line from the Fullerton Station or Armitage Station (depending on where you are in Lincoln Park) to the Roosevelt Station and then take the 146 Bus to Soldier Field or walk the remaining way. If you take the Red Line and the Bus it should take you approximately 40 minutes. If you walk the remaining way it will take you a bit longer. The fare is $2.25 for Red Line and $2.25 for the Bus. The cab fare would be approximately $23. Google Maps is great to use in Chicago for planning your route. It will show you routes based on car, public transportation or walking. There are also a lot of taxi fare estimators online (such as faxifarefinder) that you can use to estimate how much cab fare would be in Chicago. Hope that helps!