The HI at the Merchandise Mart can be a convenient (and relatively inexpensive---for a Loop hotel) place to stay, but only as long as there is not an event going on at the Mart. That excludes the second week in June and a couple other dates.
To the OP, if "walking distance" is your primary criteria, you might consider a hotel in the O'Hare area. There are a number of hotels within close range (truly "walking distance") of the Cumberland and Rosemont CTA Blue Line stations, which are accessible from the Clinton/Blue station 2.5 blocks from Union Station.
I would not recommend walking to any hotel around Union Station with luggage in tow, as the sidewalks and curb cuts are not always even (much less smooth) and the streets are often pedestrian heavy at many times during the day. Crossing the bridges can be challenging even fully ambulatory during times of peak traffic. This is even more of an issue if it happens to be precipitating when you are trying to get from Point A to Point B. Best to take a cab or Uber/Lyft if burdened with more than a backpack/shoulder bag.
As mentioned, hotel rates in Chicago vary widely, and as with much of the northern US, are higher in the high season of summer. Still, deals can be found, particularly on weekends and near holidays (I stayed at a O'Hare area hotel around Independence Day this year which was $84-94 for several nights that week, compared to downtown hotels which were $200 & up for the same time period).