If you are starting your camino in Oviedo be sure to leave enough time to visit the Cathedral, which is the origin of the camino itself. It is also the place to pick up your credential (pilgrim passport) which will cost you 2.5€ but will include a visit to the Camara Santa, the oldest part of the Cathedral which was originally built to secure relics.
The greater Oviedo area is home to more pre-Romanesque architecture than any other place in Asturias; including the Iglesia de San Julián de los Prados, Santa María del Naranco and San Miguel de Lillo. These last two are not in the city center, but instead require a small detour when leaving Oviedo on the way to Santiago.
On the other end of the spectrum is the ultra-modern Palacio de Congresos by Calatrava, and in between the oldest and the newest are dozens of churches and civic buildings of note. The Monasteries of San Vicente and San Pelayo are the most noteworthy.
Arriving along Camino San Salvador: Shells and arrows will bring you right into the old quarters of Oviedo, passing a plaza and the beautiful Ayuntamiento building. There is talk of a new certificate which you can claim upon completion of the route, but details of where to find it are not yet sorted out. For now, you are advised to ask in the Cathedral or in the Albergue de Peregrinos.