Near The Venue
Get Coffee
Dollop
A proper hipster coffee shop serving beans from one of the better local roasters, Metropolis Coffee. The best in the neighborhood by a fairly wide margin.

It's a bit of a hike from the venue, so you might want to combine it with lunch. Luckily they have solid food, as well.
Good For: Cortados, Pourovers, Cold Brew, Breakfast, Lunch
Dollop
Medici on 57th
Medici on 57th is a legendary Hyde Park coffee house and restaurant that has been frequented by U of C students and locals alike since the 1950s. Solid food, pastries, and bottomless coffee in a cloistered, wood-paneled atmosphere that'll make you feel like studying something. The art collection alone is worth the trip.

Combine with a visit to 57th Street Books a few doors down for a quintessential Hyde Park experience.
Good For: Lunch, Bakery, Families, Outdoor Patio
Medici on 57th
Piccolo Mondo
Situated very close to the Museum, this is great place to grab a nice lunch or dinner, or a quick coffee or pastry. Italian cuisine "with a touch of tapas from Spain", plus an Argentine bakery.

A Hyde Park fixture for 3 decades, Piccolo Mondo isn't going to change your life, but it's definitely a legit dining spot, and very convenient.
Good For: Lunch, Dinner, Coffee, Convenience
Piccolo Mondo
Sip and Savor
Good coffee shop run by nice people serving fair trade beans.

The thing that stands out, though, is the fact that they offer shots of booze IN your coffee (or your smoothie, evidently?) - Baileys, Kahlua, Rum, and more.

So if that sort of thing appeals to you, head on over to 53rd and Hyde Park Boulevard for a Caffeine Mixer at Sip and Savor.
Good For: Coffee, Hair of the Dog
Sip and Savor