I will be sleeping 3 nights in Fussen then drive to the Grimmelwald-Murren area. What is the best driving route?
Try this, http://www.viamichelin.com/
You are aware of all the in and outs of international drop charges on rental cars, Austrian and Swiss vignette sticker requirements, parking the car in a garage in Lauterbrunnen, etc.
Just to add a bit to Sam's comments ; I use both rail and car travel overseas . The route and practicality determines which mode . In this case a car gets you nothing but a 5 -6 hour grinding drive . The train station in Fussen is in easy walking distance from the center of the old town , and the train ride to Lauterbrunnen is relaxing with great scenery ( which you won't be able to enjoy nearly as much due to the necessity of paying attention to your driving ) . Once you reach Lauterbrunnen on the valley floor , the car becomes useless , as all the villages on both sides of the valley are car - free , so you will be paying daily rental and parking fees without any benefit . I would give this a second thought . I would always opt for a car in an area that calls out for one ( Tuscan countryside , Cotswold Hills , Scottish Highlands ) but this area is not one of them . Also , if you buy rail tickets in advance from DB on their site , large discounts are available . As an example , we traveled from Fussen to Brig , Switzerland this past October , for 36 EU each as opposed to 140 EU each by buying in advance .
There's really only one feasible route that you can do in one day. It doesn't look far on a map, but it takes much longer than it appears. Head towards Lindau, and consider stopping here for lunch. Swing around the southern edge of the Bodensee. You can avoid paying for a transit vignette in Austria by driving on the secondary road through Bregenz, but this will really slow you down. And you need to buy a separate vignette for Switzerland anyway. Head towards Zurich. You can either drive further west through around the city on the Autobahn, or cut through downtown. Even with traffic, both options take about the same amount of time. Shoot south towards Zug and Luzern. Take the mountain pass further south and you're just about there. The route is plenty scenic.
Is this the same person as yemanlw posting on Germany? If so, looks like he's picking up the car in Austria, so he will already have the Austrian vignette.
As has been said above, check the routings from viaMichelin or on of the other routing sources. The drive is on the slow side but the scenery is well worth the time. Unlike a train, with a car you can pull over and stop to really take in some of what you are going to see instead of just having it blow by. The Austrian autobahn vignette can be purchased for a short duration and is not that expensive but the Swiss one is only for one year and costs about $40 but get them at or kust before crossing the border as the fines are steep. So many people lie to whine about the coat of parking in Lauterbrunnen but they ignore the simple solution, stay in Lauterbrunnen. Every hotel I have stayed at in Lauterbrunnen has had free parking available. Take the aerial tram up to Murren and enjoy the town that way. Frankly, Gimmelwald is overrated in Rick's books. There are a lot of sights to see in the area and using Lauterbrunnen as a base with a car makes like a whole lot easier.