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Connecticut CT New Haven 06511 Self Storage Units in New Haven, CT, 06511 U-Haul Moving & Storage of Wooster Square 1,496 reviews 83 Water St New Haven, CT 06511 (203) 936-6913 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.