Marbella Pueblo or downtown Marbella is near the charming old town; it is clean, residential, quite beautiful and classy. And cheaper than Puerto Banus, much cheaper.
In my opinion, this is also the best area to stay for those looking for active nightlife.
You can stay anywhere in Plaza de los Naranjos, Calle Aduar, or Calle Alcantarilla. Just map the hotels that you like along this area and you will be fine. Also note that Marbella is a pretty long city so make sure that where you are staying is close to the old town or downtown area - it is quite common to be told that your hotel is in Marbella but then you discover that it is in Marbella but 20 km further away from where you imagined it to be.
Marbella downtown hotels
El Fuerte is a nice old hotel on the beach by the promenade in Marbella. Other reliable options are Hotel Princesa Playa, Linda, or Don Pepe.
Just be aware that if you are looking for peace and quiet, avoid Marbella during the second week of June when the Feria happens and the place gets just as noisy as Puerto Banus.