Oh yes, the U of C student's call for better restaurant options in Hyde Park- if I had a nickel for every time...I'm at the U of C as well, and here's my recommendation.
Can't really speak to the delivery part of your question- I'm really only familiar with Hyde Park proper as far as that is concerned, and I'm afraid there really isn't much the neighborhood has to offer beyond decent (aside from Z and H). But I would definitely recommend checking out (and calling to see if they deliver, if you have your heart set on it) some places in Greater Grand Crossing especially on 75th St. Army and Lou's is a great Chicago institution for soul food. A block down is Soul Vegetarian East, which gets very high marks as far as vegetarian/vegan places are concerned. In fact, there are quite a few places in this vein in the neighborhood, including Yah's, another vegan soul food restaurant that did pretty good renditions of imitations like mac and cheese and bbq nuggets with a very fun and helpful staff, and a vegan taco place that I'm still trying to find that was recommended to me by someone at Yah's. Still yet on 75th is Wings around the World, which is a very fine takeout only establishment with a great selection of wing flavors with a flavor profile and crisp easily a league above Buffalo Wild Wings. And Lem's, yet another place on 75th, is supposed to do pretty good bbq, although it probably gets too often overlooked for the outstanding Barbara Ann's, which sadly is on Cottage Grove and 76th St. Yassa's does very good African on 79th, and while I've never been, Izola's is just a couple blocks down and is another soul food institution. And I'd be remiss not to mention Dat Donuts, who, on a particularly auspicious culinary day, piped out hot fresh Dat Donuts the size of a tire rim just as we got there. If you can time up your trip right or call them to make sure they'll have a batch fresh when you get there, you will be rewarded with a donut that is simply lighter than air- hot, pillowy, and delicious. If donuts are your thing, a little walk from Hyde Park on 47th is Abundance Bakery, which does a mean, mean apple fritter.
I'm gonna guess that most of these places don't deliver. But they're certainly worth going out of your way for. Greater Grand Crossing has quite the culinary treasures, with any one of these places exceeding any place in Hyde Park. But you got to work for your culinary adventures from Hyde Park. A drive down 47th can take you to goat heaven or hearty one dish taverns (Birrieria Zaragoza, Stanley's Tavern), down 55th to a wonderful greasy spoon breakfast near Midway (Sammy's Kitchen) or down 63rd to an innovative culinary school restaurant (Sikia). All of these places, I may add, have some of the nicest people that will take care of you like family.
Unfortunately, Bronzeville, Woodlawn, and Englewood don't have a tremendous amount to offer, so you need to open your scope beyond these neighborhoods. Greater Grand Crossing is a good start, and jbw has the right idea with Bridgeport, Chinatown, and Pilsen recs, although I would certainly begin to explore Little Village if I had a car. Hope this is helpful- you have to have a certain amount of daring, creativity, and adventurousness to find and get to some of the places, but no one said the U of C was going to be easy, right? Guess it goes for seeking out culinary gems, too?
-T Kent