There are a lot of public places. If you are south Montgomery; start at Fort Washington State Park, Norristown Farm Park, and Pennypack Creek.
middle Montgomery; Evansburg State Park, Skippack Creek, and Perkiomen Creek
north Montgomery; Greenlane park,Swamp Creek, and Pennypack Mills County Park
And if you are willing to drive to Buck County, Peace Valley Park and Nockamixon State Park.
Personally to me, the best way to find morels spot is to Scout an area after the rains. The day after the rains, you will actually start to see many signs of potential morels. Half Free Morels, Dryad Saddles, Oysters, and other mushrooms. Again, DONT pick any morels if you find them after the rain. Let them grow. Morels typically grow for 5 to 10 days before rotting (depending on weather). If you do find morels after the rain, be smart and hide them by putting some leaves on top of them and mark the area so you know. Just dont litter.
Look for your typically ideally spots Apple, Tulip Poplars, Elms and Ash tree. Look for those trees in clusters and good luck.