Parking can be tricky at Muir Woods. Sometimes you have to take a shuttle.
But I have a much better idea than the standard tourist plan for Muir Woods: do a hike down to Muir Woods (and hike back up). Here's the route:
http://www.mapmyrun.com/routes/view/746981579
This 4.5-mile loop hike is extraordinarily beautiful. Muir Woods proper, the lowest part of the hike, is fantastic, but so is every other part. Redwoods galore.
Parking is a breeze if you do this. From the GG Bridge, take US-101 North to the Hwy. 1 exit. Highway 1 uphill to the right on Panoramic Hwy. Take Panoramic for about 3 miles. Go straight at the Muir Woods Road intersection (signs for Muir Woods tell you to turn left). Park either across from the Mountain Home Inn, or if that's full, on a dirt road just north called Gravity Train Road.
Here's a close-up map.
Enjoy! It's a hike you'll never forget. There's a cafe at the Muir Woods visitor center if you want to get a meal/snack half-way through.