Tenerife is great for walking at most times of year, apart from perhaps the summer when it can be hot. Spring is particularly good as the flowers will be in bloom and the weather is usually fine with good temperatures. If you are going to be relying on public transport to get around, Puerto de La Cruz in the north is probably the best for access to the best walking areas. The main areas for walking are the Las Cañadas National Park around Teide for volcanic scenery, the Orotava Valley for pine forests, Teno Mountains in the west and the Anaga Mountains in the north-east. This last region is, in my opinion, (and lot of other walkers) the best region for stunning mountain scenery. It is a Unesco Biosphere Reserve and is characterised by steep, forested mountains and deep barrancos (ravines). Having said that, most of the island has impressive scenery away from the big resorts on the south-west coast.