Technically it's not the Loop but 444 N. Michigan has exactly what you're describing although I wouldn't call the gym "small." (Then again, I'm obese and am depressed by gyms so maybe I'm not a good judge of that?)
321 North Clark has a great gym with towels :) and dedicated indoor bike parking spaces.
For safety reasons management makes you enter through a loading dock (requiring an elevator ride) rather than the drivers' entrance but this little hassle is offset by the security and overall conditions of the bike parking area.
The only downsides to this location are not building related issues. Carroll Street, which runs under Kinzie, has unused railway tracks right down the center of the street. More than a few of us have gotten injured after getting caught in the track. Also, the parking valet services that rent space on Carroll Street - including Lux and the Westin Hotel - abuse their parking rights and drive at ungodly speeds up and down the ramps, threatening bikers, pedestrians, and other drivers.
150 N Michigan has a small bike room, which, I'm told fills to capacity (12 or 15 or so?) in "the season" but so far this year I've never seen more than six or seven bikes in it, and really could be there be more perfect riding weather? There is currently no gym, but I'm told the building management plans to add one this summer. Access to the bike room is either through a loading dock rigmarole OR via a Pedway entrance - you have to carry your bike down some stairs, but it is much simpler than the loading dock/elevator option. Amazing views!
I believe 2 N LaSalle has a bike room, though no gym that I'm aware of.
I used to work in 221 N LaSalle, which had a small bike room off the parking garage (alley entrance, exit onto Lower Wacker, key access to room) and an adjacent gym. At the time, there was an annual fee for the bike room and a reasonable monthly fee for the gym. I believe management has changed since then, so it's possible that policies may have changed. I think that building may be condo now - now 100% sure.
My last job was at 55 W Monroe, which has a small bike room and adjacent gym with showers on a floor above street level, with access via alley (loading dock) and freight elevator. Bike room access was via swipe card - special permission added by application to building management to a standard security card - very secure, because few had access. I don't recall the $ for that one, but I think it was minimal.
I work at 200 W Madison St. There are two bike areas, one completely enclosed and an overflow area within bars accessible from W Calhoun Pl (the alley between Madison and Washington). There is a gym with showers available to tenants at no charge.
30 North LaSalle has a bike room. It's pretty bare bones, but it's free. There is also a gym with showers, though I've never seen it. The gym has a monthly fee.
Not directly responsive but another approach for consideration. Look at Prudential 1&2, Aon Center and BCBS Building...All across the street from the McDonald's cycle center.
200 S. Wacker. Has a small gym with showers and towels, accessible with a one-time fee (I think $50 or $70). Bike parking inside the building off the parking dock and in the gym.
Only downside is getting bike to/from loading dock involves using a staircase from street level down to loading dock.
Also has bike parking at the building at street level.
Though I'm not sure of the current status, a few years ago when I worked for the Sun-Times, the building had implemented a space for bicycles, lockers & showers. Location is 350 N. Orleans, just outside of the loop.
See photos below.
I know Merchandise Mart has something similar, and they have a Gym inside too.