Auburndale Cove has plenty of parking and is delightfully shady, and breezy right on the Charles River. 

Take West Pine Street to the end; there's plenty of parking on your right in a huge lot. Turn left after walking/wheeling into the park; we're in Picnic Area One beyond the yellow tape. There is no grilling allowed this summer, but the City of Newton gave us permission to use the location for our classes.