This is one of the 14th Spanish National Parks and it is located in the island of Tenerife. It comprises the Mount Teide, highest mountain in Spain, and some areas around it.
I did not try to climb the Mount Teide till the top when I was there but it does not seem to be a very hard task. Just take into account that the summit is at almost 4000 meters therefore lack of oxygen can be a problem. You should also take into account that all the territory of the National Park is over 2000 meters high therefore weather can be quite different than in the rest of the island.
Landscape in Teide National Park is vulcanic and there are some endemic plants living there. Inside the Park there is one Parador, that would be a very good choice to stay as hotels of this group are among the best and most charming ones in the country.