Trish,
I'd considered staying at the Granada Parador but it was completely booked when we were there in October 2015.
The Parador is located at the Alhambra complex and it looks very nice but it's also expensive.
We ended up staying at Hotel Anacapri, one of RS recommended hotels, very close to Plaza Nueva & the cathedral.
We also considered staying at the NH Collection Granada Victoria, but it's a bit further from the city center.
There are more recommendations on Rick Steves' Spain guidebook. You may find a copy at your local library if you don't want to buy it.
Going in March
You're going next month?
I do hope you've already booked your tickets to the Alhambra.
There are still tickets available for most of March, except for March 4, 7, and 28-31 which are already sold out.
Have a wonderful trip!