Favorite thing: If you are one of the many pilgrims that passes through the town or wanting to save pennies at lunchtime then take a picnic to the pretty park (origin of the name?). It is built into the roman wall, has shade, a purpose built graffiti wall and a pretty view of the plains below. Look out for the madroño donado trees planted with funding from Madrid...the tree (and a bear) is on the capital city's symbol.
The cathedral and Gaudi palace are the most famous attractions of Astorga, but the whole city centre is full of sightseeings.
Take a city map from a tourist office or the pilgrims hostal (like the picture) and go round the streets to see all the marked monuments, as well as enjoy the sight from the city-wall promenade (Paseo de la muralla).