MadridMan has compiled a fairly extensive collection of Pamplona Apartments which have websites along with their location under each link. The apartments are mainly holiday apartments, also known as "self catering apartments", and are considered to be short-term apartments in Pamplona or long-term apartments in Pamplona. All have full kitchens or kitchenettes and many have balconies, electronic equipment, internet connection, air conditioning, and many other ammenities.
One can read reviews and recommendations of several of Pamplona's lodgings in the "Hostels & Other Lodgings" forum of MadridMan's ALL SPAIN Message Board. One should consider choosing a location somewhere in or near the old city center; somewhere around Plaza del Castillo, Plaza de Toros, or Plaza del Ayuntamiento.
Please keep in mind that if you have decided to find lodging for the "Running of the Bulls" in Pamplona during the San Fermin Festival you'll need to make reservations FAR in advance - even as much as one year ahead of time. Also be prepared to pay double, triple, or four times the regular apartment rates during San Fermines in Pamplona. If you do decide to run with the bulls in Pamplona, be safe, be sober, BE SMART, and HAVE FUN!