Don't try looking for apartments in Tucson, or anywhere else in Arizona, in what might be considered the dead of winter in more northern states. So many people from northern communities head to Arizona during the winter that the rental market becomes very tight. Look in the summer though, and you should have your pick of apartments.
Remember when applying for apartments that not all landlords are created equal. Ask your landlord if they live in the building, or if they don't, who in the building is responsible for looking after it if something should go wrong. Landlords who can't give satisfactory answers to these types of questions might not be the type of people you want to deal with.
The Sun Tran system is probably the best way to navigate Tucson. Although many people drive, the lack of a comprehensive freeway system causes a lot of traffic conditions that are slow and frustrating. The city also has a lot of bike paths, but inexperienced riders need to be careful of the intense summer heat when riding.
Natural beauty is readily available around Tucson. Sabino Canyon is a sight to behold, and the Saguaro National Park is a great place to see highly recognizable American cactus. The most popular dance club in town is probably Club Congress. If you just want to sit and have a drink, head down to 4th avenue and take your pick of the local pubs.