Watch traffic signs next to traffic lights. Enlarge my picture: sometimes (like in my picture) you enter one-way street.
Warning: there were quite a lot of one-way streets in Tucson. They were often wide (3 or 4 lanes) and they were almost empty when I was driving there (before sunset at business day). Remember that you drive one-way street not to U-turn on them! I... almost forgot it once there.
There are a lot of traffic lights in Tucson downtown - watch for them. In contrast to many European countries they are usually located exclusively after the crossword (intersection). In many European countries they are located in front and sometimes (but NOT always) after a crossword as well.
Exceeding the posted speed limit can get you a ticket and create an inconvenience.
The top speed limit on freeways in town areas is 65mph, out on the "open-road," like in areas past the cities, the speed limit goes up to 70 mph.
Inside the city on streets it's usually 30mph - whatch the traffic signs.
And remember: in Europe the speed limits are usually specified by law in each country (for urban areas in most countries it's 50 km/h, higher outside, on freeways, two-lane divided highways etc.); in the USA each highway/street may have its own speed limit ---> watch for traffic signs!
Cautious drivers should be aware that many Tucsonans don't stop at yellow lights. Therefore, if you stop and there is a car following close behind you, they may hit you from the back because they don't expect you to stop. Many people I know have been hit from the rear in situations like this. While it is against the law, it is often safer to go through a yellow light, even when it is changing to red.
Tucsonans are notorious red light-runners. If you're first in line at an intersection, when your light turns green--especially if you're in the left turn lane and have the green arrow--ALWAYS look both ways before entering the intersection. Some bozo is guaranteed to be flying through on red.
Nationally, Tucson ranks #4 in terms of frequencies of fatal wrecks involving light running. Mesa and Phoenix are 1 and 2, and Oklahoma City is #3. So watch it.