I've made it all the way to Tranquility Bay in my golf cart, got lost twice along the way. This was back in early December. The road turns to beach, then to jungle, then to road, then to beach again, and you're there. Takes about 1.5 hours if you're driving conservatively. We did some fishing and snorkeling up there, and on the way back, my buddy drove (without letting off the gas once, except to avoid a HUGE roadside trash fire), and we made it back in 45 minutes
Tranquility Bay, to my knowledge, is the last resort north on the island, about 14 miles north of the bridge.
Since, it's rained a lot, and the roads have been pretty bad. I have yet to try again, but am planning to take a trip way up north via golf cart to collect all the sandals that fall out the back of carts (for a project a friend is working on).
I'll report the conditions soon after!