The Camino del Salvador is 121 km. from León to Oviedo. The refugios are, however, not ideally spaced for walking this in manageable stages, since they are at 40,49,, 74, 97, 111, and 130 km. from Leon.
There is other accommodation available along the route, but this again is not ideally located. The second and thirdd stages from Buiza over the Cordillera mountains to Pajares is 25km; we haver split this into 2 stages because it is fantastic mountain scenery, takes longer than you might think, and we liked to enjoy it.
If 42 km. of fairly level walking seems too much, good alternatives are to spend half a day sightseeing in León, and then walk to Cascantes, which has 4 buses a day to and from Leon So it is possible to get a bus back to León that night and then get a bus out again in the early morning to start walking to Buiza. Another alternative is to sleep in one of the many hostals in La Robla (likely to cost around 20 euros).