The answer to this question is complex so I will answer with a short answer and then give more info.Short Answer:
Most of the hotels in the most interesting places right in the centre don't have their own parking.
Even if these hotels do have their own parking it can be complicated to get there due to narrow complicated streets.
A way to side step the whole issue is to park in the Severa Ochoa car park which is very easy to get to, has good prices for long stays (especially over 48 hours) and you can then get to any hotel with a short walk, bus ride or a taxi.
In this way you don't have to base your choice of hotel on the availability of parking.
Here is Info about Severa Ochoahttp://granadamap.com/so/index_en.htm
A hotel which is right in the old part of town which has parking next to the Hotel is Hotel Casa Morisca.http://granadahotel.com/hotel/Casa_Morisca_Hotel_GranadaLonger Answer:
If you don't care about being right in the centre of town then there are many Hotels with easy parking.
Hotel Nazari http://granadahotel.com/hotel/Nazaries_Business_Spa_Hotel_Granada
A very good compromise is the hotel Arabeluj which also has good prices.
It is easy to get to, has free parking, is near to the Alhambra and the minibus goes past frequently which will take you to all the interesting places. http://granadahotel.com/hotel/Hotel_Mirador_Arabeluj_Granada
Another solution is the park in the Alhambra car park which is easy to get to and stay at one of the hotels near there.