Apartments For Rent In Chicago Bucktown Area . The luxury apartments for rent in bucktown, chicago can range from $1550 to more than $2550, depending on unit amenities and size. Add dates to see available apartments and rates for. 2143 W Lyndale St 1E, Chicago, IL 3 Bed, 3 Bath Condo 41 Photos from www.trulia.com An apartment unit in bucktown costs you from $925 to. 1847 w armitage ave #3r is. About 0.4mi from bucktown, chicago il view shehjad's room.