For the most part, the police can only search a car if they have a warrant. This will not stop them from asking if it is all right if they search your car during a traffic stop. You have a right to refuse and wait for a warrant to arrive if an officer is certain a crime has taken place.
You should remain calm, cool and collected during a traffic stop. You do not want to give officers any reason to suspect you committed a crime. Even if you believe they will not find anything incriminating inside your vehicle, you should still always say, "No."
You never know what an officer may find
If you are a tourist in the city, then you may use a rental car. You never know if the rental company thoroughly searched and cleaned the car, and there may be something illegal inside that is not yours. If you try to tell the police you had no idea it was there, they are not likely to believe you. You do not have to consent to a search, so you should not willingly do it.
The police could damage something
If you consent to a search, then the police may spend upwards of 30 minutes checking every inch of the car. They may not find anything, but they may be careless when handling your personal belongings. You will be out of luck if an officer ends up damaging something valuable.
You protect yourself in court
By clearly refusing a search, you protect yourself in court in the event the police decide to search your vehicle anyway. There is not much you can do if they force you to step out of your car and search your vehicle. However, in this instance, anything illegal they find cannot come up in court. They obtained it through unconstitutional methods, so you have a better defense in court.