What is the best route to take from San Francisco to Healdsburg in order to hit some wineries and enjoy the views.

If you want to see redwoods, stop at Muir Woods along the way -
http://www.nps.gov/muwo/index.htm

My favorites in Sonoma -

Winery - Truett Hurst -
https://www.truetthurst.com/
Store - Dry Creek General Store - great for picking up things for a picnic -
http://drycreekgeneralstore1881.com/
Non-wine - Dry Creek Olive Company -
http://trattorefarms.com/

Gorgeous views - we drove up to Lake Sonoma
http://www.parks.sonoma.net/laktrls.html

I usually tell friends to buy a "MapEasy's Guide to Napa/Sonoma at your local bookstore...if you still have a local bookstore.
http://www.mapeasy.com/destination_city.cfm?location=61
Or order it on-line.
Just make sure it's as current as possible.

Shows most wineries, hotels/motels, restaurants, shopping etc.
The one for SF and the Bay Area is good, too.

Head up 101 to Petaluma. Once there, head west over to Bodega Bay and have a bite to eat. Go north on Hwy 1 to Jenner, at the mouth of the Russian River, where you will catch Hwy 16, east along the river. Along here you would be able to visit the Armstrong Redwoods grove near Guerneville.

Just east of Guerneville, the road splits. Take the River Road where you can visit Korbel Champagne Cellars. Nice cafe also.

By this point, depending on the time left in the day, you may want to then head east and catch the Eastside Road up to Healdsburg. If you have a lot of time left, or save for another day, take the Westside Road. Lots of wineries to visit along both. Westside Road eventually ends up in Healdsburg and Eastside Road near 101 out of Windsor.

Check out a map of this route.

Your title should actually be Healdsburg. Sonoma is a different town in the other direction. Sonoma is also the county both cities are located.

I see from your other thread that you are heading up north along the coast. Skip the Armstrong Redwoods as you will see better up north. Perhaps skip my plan all together or do a potion of it.