IF you had to choose 2 places downtown
Kiki's Bistro for French Bistro
The Paramount Room for a more funky, eclectic spot--best sweetbreads that I've had in Chicago.
La Scarola for old school Italian American done very well in a great storefront atmosphere. It was Joey "The Clown" Lombardo's favorite restaurant in the city before he had to go on the lam.
There are so many places to choose from, it is hard to make a recommendation based on just places with an entree $25 and under.
But, going just on price and within about a mile radius of Navy Pier (which is my definition of "downtown") I would recommend Green Zebra and Francesca's on Taylor.
If you are interested in venturing further north into more of a neighborhood, I'd recommend Volo in Roscoe Village (wine bar with great food) and Cafe Matou in Bucktown (french).
Green Zebra is not downtown (it's almost three miles from Navy Pier) and it's worth noting that it's almost entirely vegetarian. Francesca's on Taylor is not downtown, either (it's also a good three miles from Navy Pier). We have some really good Italian restaurants here but I find the Mia Francesca chain (about 16 local restaurants) to be just okay and nowhere near as good as our best mid-priced Italian restaurants (like Cafe Spiaggia).
I ate at Cafe Matou last year and I was really disappointed. If you happen to live in Bucktown, you might consider it, but it's really not worth traveling to. If you want a French bistro in the stated price range, you can get much better food within the OP's stated budget at Bistro 110 or Kiki's Bistro. And both of these are downtown, too.
1. A Mano, small plate Italian. Half orders of pasta, and great antipasti
2. Opera - South Loop - On Sundays and Tuesdays $28.95 Three Course Prix-Fixe Dinner choose any appetizer or salad, and any entree and any dessert. Menu link below. I cheated on the $25, but it's a great deal.
More information would help us make the best possible recommendations for you. But going by $25 pp including tax and tip, there are two places that I would recommend -
615 W. Randolph
Spectacular Mediterranean cuisine, with excellent value offered for the price point. There is communal seating and it gets pretty loud so it is not the right place for an intimate dinner. They do not take reservations so avoid peak days/hours.
Lao Sze Chuan
2172 S. Archer
A bit further south than 'downtown' but worth the trip. Best Chinese in Chicago hands down. Again, excellent value offered. Every time I eat here (which is quite often), I find myself craving more the next day.
I'm sure that nsxtasy will offer many excellent options as well, you can't go wrong with anything he suggests.
When you say $25 per person, do you mean entrees less than $25 each, or do you mean $25 including more than one course, and including tax and tip? And does this have to be for dinner, or can it be for lunch?
I assume by "downtown" you mean not only the Loop, but also the surrounding neighborhoods, i.e. South Loop, West Loop, River North, Michigan Avenue, Gold Coast, Old Town, and River East.
That budget, at dinner, rules out our best contemporary American restaurants (e.g. one sixtyblue, Aigre Doux, Blackbird, North Pond), whose dinner entrees tend to be in the low thirties. But there are some very good choices available in other categories.
My first pick would be Cafe Spiaggia, for Italian food. We have several excellent Italian restaurants in the downtown area, but while some (e.g. Coco Pazzo, Vivere) are slightly above your target price range, Cafe Spiaggia is right where you're looking for. Note - don't confuse Cafe Spiaggia, the mid-priced casual Italian restaurant, with Spiaggia, its sister restaurant next door, which is very expensive and dressy. www.levyrestaurants.com
For the other choice, I would choose one of our upscale ethnic restaurants, whatever kind of food sounds most appealling to you; here are some possibilities, and all are in your stated price range:
Frontera Grill (Mexican) - www.rickbayless.com/restaurants
Vermilion (Latin-Indian) - www.thevermilionrestaurant.com
Le Colonial (Vietnamese) - www.lecolonialchicago.com
Red Light (Asian fusion) - www.redlight-chicago.com
Mercat a la Planxa (Spanish-Catalan) - www.mercatchicago.com
Carnivale (Latin fusion) - www.carnivalechicago.com
Aria (global fusion) - www.ariachicago.com
Vong's Thai Kitchen (Thai) - www.vongsthaikitchen.com
Cafe Iberico (tapas) - www.cafeiberico.com
I believe all of the above accept reservations on opentable.com with the exception of Cafe Iberico, which doesn't accept any reservations for groups smaller than 6, and Frontera Grill, which does not take reservations, except a small number of same-day reservations when they start answering the phone at 8:30 am.