You may want to look at Fort Lee. The NJ Transit 158 bus runs from Fort Lee to Weehawkin.
Fort Lee has good schools & is a nice, walkable town with many highrises.
You may also want to look at Edgewater, also on the 158 bus line, but much closer to Weehawkin. Edgewater has its own schools until high school than the kids go to Leonia High School (a good school.)
To look at transportation options:
www.njtransit.com Try using either "trip planner" or "service near a location" function.
Also Light Rail:
New Jersey Transit
Just noticed that you want a yard, not sure if you'll find that in these towns. Try Leonia.