Savings: It costs about 1,000 euros to buy a trekking bike and proper equipment. After you make that investment, the bike will quickly pay for itself in lower travel costs and, if you pack a tent, also in accommodation costs.
Remember this: The destinations accessible by bike may not be well advertised, so they may be difficult to find. Your fitness improves as you get used to cycling.
Reducing your carbon footprint: Cycling rather than driving a 100-kilometre trip only has a small impact on your carbon footprint.