Best Road/Hwy. to drive to see the Northern Lights?

when are you going?

Mid-November for 4 nights...

Four nights? Good luck.

Do you buy lottery tickets?

Before investing in your trip, you might want to read this: Northern Lights

Do you feel lucky?

There is no detailled route that can be planned, as they are a natural phenomenon. You need to get out into the countryside late at night - we were advised that 11pm to 2am was the best time to look and if you have a week, you may see them once, which we did, on our last night. You need a night with clear skies, of course, so wrap up warm.

I would just add that: driving is not a good way to see much of anything in the sky...

1. It's dangerous. When driving, DRIVE. That requires your full attention. Especially at night, in a foreign country. Don't zoom down the road with your eyes on the sky, someone is gonna get killed (perhaps you).
2. While driving, you're not going to see squat in the sky anyway. The lights inside your car, your headlights, and other light sources will destroy your "night vision" which you will need to see faint things in the sky. It takes while for your vision to adjust to darkness.
3. To have any chance of seeing aurora, you need to get as far away from all lights as possible.

I would suggest getting reviews of tour companies and doing a tour the 1st night you are in Iceland. Many of them offer free tickets for subsequent nights until you are actually able to see the Northern Lights. The phenomena depends on a number of factors and they are not easy to predict.