There are several Green P lots (municipally operated parking lots) located right around the Royal York (see map at left; for current prices, visit the Green P website) and search "100 Front West".
Another option is valet parking provided by the hotel. Self-parking is available under most of the nearby office buildings; 79 Wellington West is one of the closest. Another resource is this website, which lists both municipal and private parking.
Maple Leafs Regroup! July 1‑4 2016