I've lived next to a public course for the past 15 years -- in a newer neighborhood with no playground. There is no mixed-use provision for this course, but that never stopped the neighborhood kids from playing football in the middle of the 13th fairway.
Early and late in the day, the neighbors use the cart paths for walking and jogging; in the winter, the fairways are used by Nordic skiers, the hills are for sliding, and there's a hockey rink, with goal nets, on the pond next to the 10th hole. Fortunately, we've been mostly spared from snowmobiles.
Public courses would be smart to devote some nearby land for a ballfield/playground if they want to keep the neighborhood from using the only available open space for purposes other than golf.