**brian**

The most direct route from Grove St. would be

Marin Blvd to Hoboken
Left on Observer Hwy
Right on Madison to 15th St
Right on 15th St
Left on Park Ave
Right on 19th St
becomes Harbor Blvd
bear right on Port Imperial Blvd (Weehawken)
merges into River Rd (Guttenberg)

You can take River Rd all the way up to GWB, but the last mile or so south of the bridge is not the greatest: narrow road, heavy traffic, bad pavement, and a steep climb at the end (though the last bit of the climb you can do on the new bike path, from Henry Hudson Dr up to the Bridge.)

A good way to avoid that unpleasant bit at the end is to turn left off River Rd onto Gorge Rd in Edgewater, then turn right on Palisade Ave - that takes you all the way to Bruce Reynolds Blvd (turn right to the bridge).
Gorge Rd is one of my favorite local climbs - about 180 ft @ 8%, with shallower grade for a while after that.

The route above is pancake flat with one big hill (either Gorge Rd, or the end of River Rd).

Another option - less direct but a nicer ride:

Newark Ave west (with a short, steep hill)
Right on Palisade Ave
Continue on Palisade several miles, to 43rd St (Union City)
Right on 43rd St
Left on Boulevard East
continue on Blvd East to North Hudson Park, then bear right on Woodcliff Ave
Right on Palisade
continue to GWB (right on Bruce Reynolds)

This route has lots of rollers, great views of the city from Boulevard East, no big climbs. A little less car traffic if you're riding at a busy time.