A couple of my favorite Chicago places come to mind - not the super-upscale places you mention wanting to avoid, but a step down from that, with superb food that will still make you feel special:
North Pond offers its exquisite setting in the middle of the park facing its namesake pond and the skyline looming overhead. Request seating in the front room with the full-length windows, but even the rear room with the open kitchen is fun. James Beard Award-winning chef Bruce Sherman's cooking is always great; his technique is to present multiple items plated together, and chances are you'll like all or most of them.
Band of Bohemia offers its own unique Bohemian decor, and the food is excellent. (They offer an a la carte menu as well as a tasting menu.) You can make it a little more of an adventure by taking the Metra train to their door.
Riffing on another out-of-town suggestion above, traveling a distance to another city makes the destination particularly special. I love dining in Milwaukee; the food is great and it tends to be significantly less expensive than Chicago. My favorites there include
Sanford for an upscale meal you say you're trying to avoid (sorry, but had to mention it),
Odd Duck for creative small plates (reservations are essential),
Dan Dan for Chinese food better than anything in Chicago,
Third Coast Provisions for seafood, and
Blue's Egg for breakfast/brunch.
If you want to go to a smaller city that is less traveled, consider Fort Wayne, three hours drive. They have a significant Burmese minority with restaurants highlighting their cuisine. For more mainstream American cuisine with global influences that is consistently outstanding, go to
BakerStreet. I've been dining there with friends every three months for the past five years, and we never consider anyplace else because it's always been so terrific. Tip: They always have an off-menu special of prime rib, and it's the best prime rib you'll ever have.
Wherever you go, make sure you mention your special occasion when making your reservation.