The places are not in order because it is quite difficult to do as all of them are different and nice in many ways:
1. Madrid and surroundings
Madrid is the capital and has a lot of beautiful monuments, buildings and streets. It has some of the best known museums in the world and it has a great night and day life with very nice restaurants and bars. It is also near the mountains where you can visit nice villages like La Granja, Manzanares el Real or Buitrago de Lozolla and you can also ski. There are also important towns as Avila (with some of the best walls in Europe), Segovia or Toledo.
It is a nice place to visit with important museums and buildings, my favourite is modernist Gaudí, Parque Güell, or different Gaudí buildings, like La Casa Batlló. Barcelona is near the sea, with great nightlife and very cosmopolitan.
3. País Vasco
are three important cities: Bilbao, SAN Sebastian and Vitoria and
also important villages like Getxo, La Guardia and Zumaia. It is a place with a
very important gastronomy (pintxos, fish and meat), beautiful coastal
landscapes and strong culture.
4. Roman vía de la plata (Roman Silver Way)
It is an
ancient commercial and pilgrimage path made by Romans. The
original way went from Cádiz in the south of Spain, to Gijón in the
north, culturally some of the main places to visit due to their
UNESCO heritage are Merida (Roman city), Cáceres, Salamanca, Zamora
and León. Last ones are very interesting
due to their cathedrals and old city. The gastronomy and the wines
are very important in these areas: torta del casar is an original and
strong cheese from Cáceres, lamb from Castilla
and really good wines in Leon and Zamora.
Leon has an amazing city centre that is also great to have a drink,
because the pintxos are free with each drink.
5. Canarias (Canary Islands)
I recommend a tour, because all the islands are different, some have very good beaches, others have very special landscapes, like Lanzarote, others have more nature to walk, like El Hierro and Tenerife hast the highest mountain in Spain, el Teide. They are also culturally different than other parts of Spain.
Spain definitely has lots to offer! These were first five of what to visit in Spain, don`t forget to come back for five more!