Yes. When they get back to her house, they open up the presents from Carlisle and Esme, and Edward. Carlisle and Esme gave her the plane tickets to Florida so she can take Edward to visit Renee and Phil. She gets really excited about that, and Edward wishes he would have let her open it in front of Carlisle and Esme. He thought she would be angry at the money they had spent for the tickets.
Edward's gift to Bella is a CD of the music he has written. It has his lullaby for Bella on it, as well as some of the other songs he writes and plays on the piano. So he gave her something without spending any money, which is what she wanted him to do. She feels really excited to have the CD. Later, when Edward leaves her, the CD is missing; he has hidden it under the floor board in her bedroom, but she doesn't know that. He took it away so he could erase his existence from her life (he also took his photos out of her scrap book).