I'll be in a sleeper, so good to hear I can get in my room at 8. I had the same idea though..what on earth will be open on Easter Sunday? I would imagine the downtown to be dead as a doornail and I'm not sure I want to wander around by myself.
Unlike Christmas,
almost anything open in and around downtown Chicago on an ordinary Sunday will be open Easter Sunday.
As to downtown being "dead", that depends on what you mean by "downtown". Except for inside the train station, the adjoining bus stops and taxi stands, and the Sears Tower just across the river (as someone correctly recommended), the area right around Union Station is all office buildings and therefore fairly dead on the weekends. However, there would be enough people arriving on Metra (the suburban trains) at Union Station and next door at Ogilvie Station heading for points east -- State Street, Michigan Avenue, Navy Pier, the museums, etc. -- that it's NOT unsafe to wander around alone, at least in a generally easterly direction.
Those areas just named would be plenty busy on a Sunday after, say, 10 or 11 am.
*State Street is 5 blocks due east. Head east on foot on any street crossing the river (if you don't cross the river after a block, you're going the wrong way!), or take any bus headed east on Jackson Boulevard. State Street is the old shopping street, with the big old Marshall Fields flagship store (I refuse to call it Macy's!) and a bunch of discount and moderately-priced shops: Sears Roebuck, Filene's Basement, Nordstrom's Rack, Old Navy, and the like.
*Michigan Avenue is two blocks east of State Street, and reached in the same manner. If you've gone due east from Union Station, you'll encounter the Art Institute at the intersection of Michigan And Adams. Just north of the Art Institute is Millenium Park, a must-see with its large skating rink, public scupltures, etc. Farther north on Michigan Avenue, across the river (
Note: the river is north-south in the vicinity of Union Station, but is east-west where it crosses State Street and Michigan Avenue), is the "Magnificent Mile," home of the fancier and trendier stores.
Towards the north end of Michigan Avenue is the John Hancock building, almost as tall as the Sears Tower but (IMHO) with a better view because it's not so closely surrounded by other tall buildings as is the Sears Tower. If you want to go directly to the Magnificent Mile or the John Hancock from Union Station, take a 151 bus from Union Station.
*Navy Pier is the city's biggest single tourist attraction, a long pier with restaurants, shops, an enormous Ferris wheel, Crystal Garden (huge greenhouse-like space), IMAX movie theater, Shakespeare theater, and various other attractions. It's a few blocks east of the Magnificent Mile, or can be reached directly from Union Station on the 124 bus.
*The Museum Campus is at the far south end of Grant Park (the lakefront park that includes Millenium Park and the Art Institute) at the end of Roosevelt Road. The Museum Campus is reachable from Union Station by taking any Jackson Boulevard bus to State Street and then a southbound 146 bus. The museums at the Campus are the Field Museum of Natural History, the Adler Planetarium, and the Shedd Aquarium. The Field Museum is the cheapest and (oddly enough) the largest and busiest of the three. Also, across the street from the Field Museum is Soldier Field. Don't worry if it looks like one of the alien ships from "Independence Day" landed in an old Roman arena; that's just the "improvement" of Soldier Field from a few years ago.
If you plan on taking a bus, pick up a fare card from the machine next to the Metra ticket office at Union Station. Bus fare is $1.75, with a $0.25 transfer good for two additional trips within two hours of boarding the first bus, but there's NO transfer without a fare card (that is, bus drivers won't sell you a transfer for $0.25 cash). If you plan on taking a lot of buses, consider a $5 all-day visitor pass, sold by the machine next to the fare card machine.
Enjoy the city during your time here!