Kensington Apartments for rent in Salt Lake City, UT on ForRent.com: (866) 398-4262 - Availability, pricing and special promotions subject to change daily. Kensington Apartments in Salt Lake City, offers newly remodeled one and two bedroom apartment homes in the heart of downtown Salt Lake City. br We've already begun preliminary work on remodeling and updating these beautiful, historic apartments which will feature exposed brick, original hardwood floors and tiles, washerdryer and dishwashers in select homes, new retro appliances, unique arches, garages, heating and air, balconies, amazing views, laundry facilities and a new fitness center is coming soon.