If you are in Madrid, take road A-5/E90 to Trujillo, then, N--521.
Some road distances to Cáceres from:
- Madrid: 302 kms.
- Alicante: 707 kms
- Berlin (Germany): 2.521 kms.
- Sofia (Bulgaria): 3.270 kms.
If you check the web, you can find some other road distances together with the best routes and driving times.
The only way to visit the Old City is walking around. There is no traffic inside the castle walls and the cobbled streets only allow pedestrians (eventually bycicles).
If you arrive in Cáceres by car, there are several parking spaces (paid) near the Old Historical Centre. And you'd better park there. I've heard some storys about breaks into cars, and you don't want your lovely trip here to be spoilt, ...