I would highly recommend the Nouzha Hotel on Abu Gfifa Street in the Benashour neighborhood, an upscale area. It's a very small hotel run by a retired Libyan Arab Airways Captain and his family.
Everyone there is friendly and helpful, much unlike the big hotels listed above. The rooms are immaculate, comfortable and quiet. The rooftop restaurant is excellent.
I haven't been there in a couple of years, but I think the place is still popular with LAA pilots and long-stay Western visitors. You'll need to book in advance.