The Atlantic Islands
I have visited the Atlantic Islands a few times at the beginning or end of the year. At this time there are a lot of migratory birds from the north choosing the Atlantic Islands as winter quarters.
Furthermore, on the Atlantic Islands you have the opportunity to see some endemic species, as Atlantic Canary, Blue Chaffinch, Fuerteventura Stonechat, Berthelot's Pipit, Iago Sparrow, Laurel Pigeon and Boell's Pigeon.
On particular Lanzarote and Fuerteventura are desert areas where there is a chance to see Cream-coloured Courser, Houbara Bustard and Trumpeter Finch.
Here are some of my favourite sites: The desert areas around Sóo on Lanzarote and Istmo de la Pared on Fuerteventura, the beaches at Morro Jable on Fuerteventura and Aeropuerto de Lanzarote, the national park on La Gomera, the mountain areas around Masca on Tenerife and the Rapil lagoon on Boa Vista.
I have also had great help to find nice birding sites in the book "Birds of the Atlantic Islands" by Tony Clark.