Answer: A big part of the draw of Big Sur is the scenery, of course, so just driving through and looking at the view is great. And then there are plenty of places to stop along the way, depending on what you like to do and how much time you have. if you are visiting Hearst Castle and then driving up to Carmel the first day, try to get the first tour of Hearst Castle in the morning so that you'll have the whole afternoon for the drive. The drive itself will take about 3 hours.
For stops, here are some ideas:
Sand Dollar Beach - nice sandy beach, short, but steep trail to the beach
Limekiln State Park - a few easy trails through a 2nd growth redwood forest, also some beach access
McWay Falls - Julia Pfeiffer Burns State park - short walk to an overlook to see the falls
Pfeiffer Beach - Pretty beach with some purple-ish sand and cool rock formations just off shore
Pfeiffer Big Sur State Park - Old growth redwood groves and some hiking - check the condition of trails online - some are still closed from a fire a couple years ago
Andrew Molera State Park - A few different hiking trails of varying difficulty and lengths, hike to a couple cool beaches.
Garrapata State Beach - Wide sandy beach accessible by stairs or short trails.