I'd be surprised if you could get out of Carmichael's with alcohol within your budget but it is a fun spot--I also think it's a bit of a haul from Union Station on foot...
If it were me, with those constraints, I think I'd go with Greek Islands--food is solid and they have party rooms--though they start at seating for 35 on the website, I'd guess they'd accommodate a smaller group if they have availability. I do suggest going the pre-purchased wine bottles/soda route and having those who want something else pay out of pocket for it--otherwise, there's no stopping someone from spending $75 just on their bar tab

. I'd bet that they would be very happy to put a package together that includes a reasonable amount of alcohol, along with a nice dinner selection.
My only other thought was maybe looking at Thai Urban Kitchen--it's a nice venue, I don't think they do a huge dinner business so, while I don't think they have a party room per se, they do have an area in the front that would likely work well for a group. The menu is conducive to ordering for a group meal of shared appetizers and pre-selected entrée options. They are basically an upscale take on Ameri-thai fusion/sushi type cuisine. I used to eat there frequently when I worked in the Loop and it was always a nice place for a business meal. Only caveat is that I haven't eaten there in a few years so no idea what the quality is like these days--maybe someone else can comment on that.
good luck!!!
"Knowledge is knowing a tomato is a fruit; wisdom is not putting it in a fruit salad." Miles Kington