Any eco tourist visiting Switzerland should spend some time at the Swiss National Park. Located on the Swiss/Italian border, this is Switzerland's only national park.
With regards to accommodation, you have a number of options. The first is to book a hostel, hotel or cottage outside of the park. The second is to stay at the Chamanna Cluozza, the only accommodation available within the boundaries of the park.
Chamanna Cluozza has stunning views and communal rooms to help keep the cost down. However, it will involve a three hour trek on foot to get there, so if you have any health problems you may want to consider one of the hostels close by such as the Sta Maria Youth Hostel. Located close to the national park there are a variety of different rooms from as little as EUR16 per night.
Now you have your accommodation sorted out, all that is left is for you to enjoy your visit. There are many trails around the park, most of which are coded. The yellow trails require no special equipment and are suitable for all. However, the blue trail will require you to be physically fit and require specialist equipment so do read-up before you go.
If in doubt, why not opt for a guided tour. There are several that concentrate on various aspects, however, with such a wonderful array of animals within the park why not try the Watch Wildlife in the National Park Trail. The tour concentrates on wildlife and plant life and includes opportunities to see ibex, marmots and deer. You will want to be reasonably fit though as this trail is 14KM and will take around 7 hours.
The Swiss National park has a strict policy regarding the environment and you should check out the park rules before travelling.