In reply to stub1984:
Around Zermatt there are various peaks that can be ascended from the valley around 3,000m - 3,500m. Camping Randa, a village before the car free tourist hub of Zermatt, is a great base. Quiet camping with easy transport around the valley if required.
As others have said, this would be great for fitness / stamina but if you want to experience altitude ( cable car journeys by themselves don't really count ) consider gaining the skills and knowledge required ( or go with an experienced partner / guide ) to climb some of the easier 4,000m plus peaks. Again, Zermatt area is good for this.