mjm,
Staying in Lauterbrunnen sounds like a great idea, as there's parking available either at the car park by the train station or possibly at your hotel. Since Lauterbrunnen is the transportation hub for the area, it's easy to explore both sides of the valley from there.
Were you planning to visit the famous Schilthorn (which was used in the James Bond movie On Her Majesty's Secret Service)? If staying in Lauterbrunnen, you could (for example) take the gondola to Grütschalp and then the small BLM railway to Mürren. Have a look around the very scenic town, and then take the Schilthornbahn to Piz Gloria, and enjoy a fine lunch in the revolving restaurant, while images of the Eiger, Monch and Jungfrau glide by the window (hopefully the weather is clear that day). On the return trip, take the Schilthornbahn back to Mürren and then down to Gimmelwald, and do a bit of a walkabout there. Finally take the gondola down to Stechelberg and take the Post Bus back to Lauterbrunnen (it's only a short trip, about 15 minutes as I recall).
I agree with a previous suggestion to skip Bern this time. You'd have to leave your luggage in the car while you're touring about, which could lead to theft (not as common in Switzerland, but it could happen).