This whole area of Lincoln Park right next to Lake Michigan makes Chicago winters worth it. Get your selfie by the honeycomb-like Education Pavilion, check out Lincoln Park Conservatory, the zoo, or just those good ole lake views. Lots of grassy areas to picnic on, or head to North Avenue Beach nearby.
We went on our first 2 dates in this area, and it has some of the best restaurants & bars in Chicago. You can't really go wrong here food-wise, but there is still no better burger in the city than at Au Cheval (no matter which other burger sits atop those "best burgers" lists). Grab a drink while you wait for your table next door at Lone Wolf.