If you really want to know what one can do in Switzerland with a car outside the beaten path, you may have a look at this older post:
SWITZERLAND BY CAR
It's perfectly possible to visit tons of gems in Switzerland by car, without boarding any train (between June and October, when all mountain roads are open).
But if you want to visit Switzerland by car, don’t choose just the places that can NOT be reached by car (like Muerren, Gimmelwald, Wengen, Schynige Platte, Schilthorn, First, Kleine Scheidegg, Maennlichen, Rigi, Pilatus, Bettmeralp, Zermatt, Braunwald, etc). Otherwise you will have to pay for both: car rental, fuel AND mountain railways.
There are tons of beautiful places in the Swiss Alps which can be reached by car. Some suggestions:
Drive from Martigny to Col de la Gueulaz on Lake Emosson (2000m/6600ft). You are then just in front of the Northern side of Mont Blanc, the highest mountain chain of Western Europe. The glaciers of Trient, Tour, Argentiere as well as the peaks of Aiguille d'Argentiere (3900m/13000fr), Aiguille Verte (4120m/13500ft), Grandes Jorasse (4210m/13800ft), Mont Blanc (4810m/15800ft) ar jus a few miles away.
Drive from Martigny to Grand St Bernard Pass (2470m/8100ft) and hike in 1 hr to La Chenalette (2800m/9200ft). From there, you have a stupendous view to the Southern side of Mont Blanc (A Neuve Glacier, Dolent Glacier, Pre de Bar Glacier, Triolet Glacier as well as a lot of 3800 to 4800m / 13000 to 15800ft high peaks). In the South, but farther away, you see the glaciers and peaks of the Gran Paradiso chain.
A easy, but very scenic 6hrs circular hike goes from Col du Gd St-Bernard via Col des Chevaux - Lake Petit Le - Col de Bastillon to the 3 blue mountain lakes of Fenetre and then over the Col de Fenetre de Ferret back to Col du Gd St-Bernard.
Drive from Sion to Col du Sanetsch (2250m/7400ft) and hike in about 2 hrs to Refuge/Restaurant La Quille du Diable on Tsanfleuron Glacier (2900m/9500ft). You are there on the top of a perpendicular cliff and can look down to Lake Derborence, just 1500m/5000ft below your feet. Stupendous view to Mont Blanc chain, Grand Combin, Mont Collon and tons of other peaks.
Drive from Sierre to Grimentz and then up to the end of the road on Lake Moiry (2250m/7400ft) and hike then in aobut 1 hr to Moiry hut (Swiss Alpine club) and Moiry Glacier.
Drive from Brig to Ried-Moerel, go by gondola to Riederalp (5 CHF/one way), hike in 1/2 hr to Riederfurka (2070m/6800ft), visit the visitor's centre/museum of the Jungfrau-Aletsch Nature reserve, walk through the Aletsch Forest and have a look at the Aletsch Glacier (longest glacier of Europe) just below and in front of you.
Drive to Breuil-Cervinia (Italian neighbourhood, 2000m/6500ft) and go by cableway to Plateau Rosa (28 EUR/35 USD roundtrip). Plateau Rosa (3500m/11500ft) is close to Matterhorn Paradise/Kleinmatterhorn (1 mile away, same panorama). The roundtrip ticket from Taesch Parking to Matterhorn Paradise would cost about 107 CHF/112 USD
Drive to Grimsel Pass (2200m/7200ft) and hike in about 1 1/2 hr to Sidelhorn (2800m/9200ft). Panoramic views to Unteraar Glacier, Oberaar Glacier, 6 mountain lakes around Grimsel Pass, Finsteraarhorn (4300m/14100ft) and dozens of other peaks. You may also hike from Grimsel Pass to Lake Oberaar (1 hr) and along this lake to Oberaar Glacier (another hr).
Drive then from Grimsel Pass to Furka Belvedere and visit the Ice cave in the Rhone Glacier.
Another road in the same area goes to Nufenenpass/Griessee. The hike from the end of the road to Lake Griessee - Gries Pass - Gries Glacier takes about 1 1/2 hrs.
Drive from Davos or St. Moritz to Stelvio Pass (2800m/9200ft). Hike to the glaciers (1 hr or so) or enjoy the view to them from Piz da las Trais Linguas (3 languages peak; 2850m/9400ft).
etc. etc.
But if you prefer to ride with Glacier Express, Bernina Express, Golden Pass Panoramic, etc. and if you want to visit Gornergrat and Jungfraujoch, you better look after rail passes.
You may have a look at
http://www.myswitzerland.com/en/home.html
http://www.swisstravelsystem.ch/en/
http://fahrplan.sbb.ch/bin/query.exe/en