There is street parking available across the street from the hotel, along Charlie Gaddy Lane. The Town of Cary Library Parking Deck, on the other side of the park, is another convenient option.
Parking is available in Pullen Park, quite close to the picnic shelter. You can find an annotated map of nearby parking options here: https://drive.google.com/file/d/1SDez9lvccN-ncyD6yLfaGjR_rzu8EECf