Basically, the most interesting restaurants, bars and pizzerias in Palermo are in the Old Town Center, known as Borgo Vecchio. There are other very nice places outside this area, but I recommend exploring this region that has a huge historic and cultural richness.
Palermo doesn’t have a large offer of hotels. There are all types of hotels in the city, but I can’t recommend any because I have never stayed anywhere else other than a Bed & Breakfast or at a friend's house. When I first went to Sicily, it was a pleasant surprise to find a charming B&B named BB22, whose owner became a great and dear friend.