Hoo boy do I have a recommendation for you: SuitSupply on North Rush Street. When you say "higher end" you won't find 4-figure prices in the place, but you can walk out with a real nice tailored suit for $500 - $600. The fit is awesome and nice lightweight fine wool fabric.
It's a small place and all they do are men's suits. Service is fantastic.
Have your suit shipped back home and you avoid the exorbitant sales tax of close to 10%.
Go to Suit Supply & get your suit. They tailor in house. Arrange to have it shipped home. Then walk south on Rush St. past the Bentley/Ferrari dealership and grab a Chicago style hot dog and a cocktail at Pippins Tavern just down the street.
SuitSupply is a Dutch company, so their sizing leans toward tall Dutch men. I normally get a 38 Tall and at this place went with a 38 regular - my arms are long and I have a tough time finding sleeves long enough without the rest of the shirt/jacket hanging off me. I'm 6' tall and I exercise and manage to keep my weight under 160. This place will not sell you an ill-fitting suit if you're a guy in shape.
Some of their suit styles are a bit wild - but they have plenty of "timeless" options and you will not be disappointed.
Then swing by Banana Republic on Michigan Avenue and get a couple of their nice slim fit french cuff dress shirts.
I love downtown Chicago and getting an awesome suit on the Gold Coast for not a ton of money - sweet.
The Village Idiot - here for your entertainment.