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Connecticut CT Bridgeport 06610 Self Storage Units in Bridgeport, CT, 06610 U-Haul Moving & Storage at Boston Ave 8,035 reviews 636-650 Boston Ave Bridgeport, CT 06610 (CORNER OF E-MAIN AND BOSTON AVE) (203) 368-2584 Hours Directions View Photos Promos 1-Year Price Lock: Monthly price remains the same for your first 12 months. 1 Month Free: Ask about our 1 month free self-storage offer with any truck or trailer reservation! No Deposit Or Admin Fee: No Deposit Required and $0.