Don't know about offroad trails....but, for me, the North Shore of Kaui is
the "bees knees".

..but when driving north on Kauai..don't just drive thru and past the
little North Shore village of Hanalei.......like most folks do... on your
way to the Napali Coast trail and snorkeling areas.

Turn right off the Hwy near the little shopping center...before the green
church on your left, and go to Wiki St and turn right again...go to the
end of the road where the public park and Pier is( a reconstruction of the
old Navy loading pier famous in the old movie, "South
Pacific" ).......from the Pier you see one of the most stunning views in
Hawaii...green mountains surrounding the horsehoe shaped Hanalei
Bay...waterfalls in the mountains (in rainy season)...and "Bali Hai" in
the distance.   Also a very nice beach to the left of the Pier.  Nicest
either very early AM or late afternoon/sunset time.  Get out...have a
glass of wine, watch the sunset, go for a walk on the beach...

In the morning, if you can get up by sunrise, there are often little rain
showers that pass thru and fill the Bay with rainbows.....TRULY MAGICAL.

Also ...from Hanalei, going to the end of the Hwy where the Napali Coast
trail starts,  there are some beautiful little one lane bridges that cross
over rivers that flow down to the ocean next to other scenic beaches.
Stop right before one of the bridges...park under some Pine trees and go
see famous "Lumahia Beach"....which can be trecherous for swimming...but
beautiful to see and walk on.

And then there's the world famous Napali Coast hiking trail...for the true
adventurers.

Warren