I like the ones others already posted (Fav's are definitely Centro and Sam & Gabes), but I have a few others to add as well - Latin King (good Italian); LUCCA (another Italian fav); Flemmings in West Des Moines (seared ahi tuna appetizer is to die for). Breakfast pastries are great at La Mie on 42nd. Fun atmosphere, fun food (tater tots, deviled eggs)at El Bait Shop -complete with a shag carpet. Great authentic German food and beer at Hessen Haus. I have to say, DSM has come along way in the past 10 years. Happy feasting!
I had a great meal at Django. Let me clarify that - I ordered $30 braised short ribs, some soup, and two beers and the short ribs came out one hour after I ordered it. They comped it and the soup and one beer. I essentially paid $6 for a $55 meal. Serious. Maybe I looked at the meal afterward more benevolently than I should have, though I don't think so. Objectively it seemed a pretty cool place with good solid food and a good beer list. I would head there.
I also ate at the Racoon River Brewery (right next door to Django and owned, I think, buy the same family, who also own the Hotel Fort DesMoines) and it was okay. Pork Tenderloin sandwich and a wheat beer. Under $10. Insanely cheap again! And local.
I don't do much high end dining. I always hesitate to respond with places I've never been, but there is very little Des Moines participation on CH.
I can direct you to places that are highly regarded by people I know, and trust.
If you are looking for places downtown, Django, 801 Steak and Chop, Sbrocco, Azalea.
A little more casual, Centro, Raccoon River brew pub, Court Ave brew pub.
If you are looking for something more specific, in a certain area, let me know and I'll try to help.
I second all of Bob's suggestions. I had a fantastic meal at Sbrocco recently. I love 801 for a classic steakhouse meal. Centro is always good and makes great efforts to use local, seasonal ingredients.
This is not high-end, but I have to give a nod to my favorite lunch spot: Tasty Taco's. There are a few of them around town and the flour tacos are pretty much a Des Moines institution. Another great place for lunch is the South Union Cafe, which is next door to Centro and has the same owners. Homemade bread and soups, hard to go wrong.
If you are staying in the western suburbs, there are primarily chains in that part of town. Downtown and East Village are pretty much locally-owned places. One of my favorite west-side spots is Cosi Cucina in Clive for Italian. I haven't been in a couple months, but Phat Chefs in West Des Moines has also been very good. Again, lots of local ingredients.
801 is great for a high-end steakhouse, but the Big Steer in Altoona has awesome steaks. There is nothing remotely fancy about, but that's kind of its charm. No frills, just good food and perfectly cooked steaks.
Also out West is Sam and Gabe's. Very nice Steak De Burgo. Steak De Burgo was invented in Des Moines, and is rarely seen elsewhere, so there's a local dish for you. Many places have a version. The classic is a beef tenderloin in a garlic butter sauce.
I haven't been to the Big Steer in years. I've tried to go a few times, but when they tell me the wait time, I end up just going down the street to the casino. Weekends are insane.