Algonquin Square Apartments for rent in Algonquin, IL on ForRent.com: (877) 791-4271 - Availability, pricing and special promotions subject to change daily. Algonquin Square offers both one, two and two bedroom plus den luxury rental living with large floor plans and condo-sized layouts. Located in the northwest suburbs of Chicago in the village of Algonquin. Minutes from I-90, Fortune 500 employment centers and the Esplanade at Algonquin shopping and entertainment corridor. Apartment finishes include: granite countertops, wood plank flooring, stainless steel appliances and washer and dryers. Property amenities include clubhouse, fitness center, business center and outdoor pool.