My suggestion for a place to stay in Granada is the Hotel Macia (a search will probably reveal threads with other positive commentaries on this place). It's clean, friendly, serves breakfast in the morning, and if you're lucky your room might have a view of the Alhambra (the front-facing ones do). It's not technically "near the Alhambra" since it lies at the bottom of the hill leading up to the palace--on the Plaza Nueva. There is, however,a cheap local bus that you can catch across the street from the hotel that will carry you up the hill. The advantage of staying at the bottom of the hill, from my perspective, is that you have access to a greater variety of places to eat, things to do, other things to see (e.g. the Royal Chapel in the cathedral)than you do staying on the hillside. It's also easier to make a trip up into the Albaicin from here.
As to friendliness, we had a very positive experience in Granada. Ate at several places with very friendly and helpful service. The people at the tourist office were also very nice.