Good choice but I wouldn’t use just Salamanca as a base, but you don’t say how long your trip is. By having only be base you could spend a lot of time returning to it after visiting wherever. With careful planning you could minimize travel time while only adding one or two other bases.
Ciudad Rodrigo was fine, but it hasn’t must see sites. We stayed at the Parador there that is the old castle. In the Parador you can climb the tower and get a great view of the city and surrounding area. Since the tower isn’t in a guest only area, there’s no reason you couldn’t visit it.
In addition to La Alberca, visit Mogarraz and Miranda del Castañar. They are close to each other and are on Spain’s list of prettiest villages. The road is very rural, but in good repair. Look up parking lots in each to save time when you arrive in town.
If you haven’t been to Ávila, south of Salamanca is Béjar. It too has some Medieval walls you can walk on. Near Béjar is a medieval bridge and the Castillo de Valdecorneja in El Barco de Ávila. Both Béjar and El Barco de Ávila are about 1.25 hours drive from Salamanca. Further south is Granadilla, Garganta la Olla, Monasterio de San Jerónimo de Yuste, and Cuacos de Yuste. Another of Spain’s prettiest villages is Valverde de la Vera.
North of Salamanca (1hr) is Zamora. It’s fairly small and can be seen in a couple hours. Further north en route to León is a very picturesque castle in Valencia de Don Juan.
Southeast of Salamanca in Alba de Tormes. The remains of Saint Teresa of Ávila are in a church there. Northeast is Tordesillas. The Convent of Santa Clara was nice to visit. There are also castles in Medina Del Campo, Arévalo, and Coca.
Cáceres is about 2.5 hours from Salamanca, so if you go there, plan stops en route to/from to make that long drive worth your time.
I could go on and on with places we enjoyed or intend to visit, but you’d need a couple months to see everything.