Your options for anesthesia are:
You are fully awake and a local anesthetic is injected to numb the nose.
2) Local with sedation
You have been given a sedative in addition to the local anesthesia. Here you may wake up and fall back asleep at times during surgery, but you will not remember.
You are fully sedated such that your breathing has to be done for you via an endotracheal tube.
You can choose any of these options based upon medical history, your comfort level, and your surgeon's preference. Some aspects of rhinoplasty (such as cutting the nasal bones) can be uncomfortable for some patients. Know your pain/anxiety threshold! But keep in mind, it is easier to recover from those options that involve less anesthesia (perhaps you have a history of bad nausea and vomiting with general anesthesia).
If you are healthy and want general anesthesia, you should not be concerned with the length of surgery. General anesthesia is like flying a plane: the tough part is the takeoff and the landing. Everything in between is automatic pilot.
However, if you are not a healthy patient, it may not be as safe to have general anesthesia because there can be more blood pressure/volume fluctuations that can put a strain on your heart and lungs. Also, if you've been told you are a "tough intubation" that might indicate that general anesthesia has a higher risk for you.
Don't feel that you have to make this important decision on your own! Your surgeon and your medical doctor will work together to determine the safest option for you. Trust them, that is what they are trained to do.