The summer is definitely the best time to look for apartments in most of Arizona, and Tempe is no exception. May is probably a good time to start looking, although starting later in the summer should yield positive results as well. Apartment vacancy is very high in Tempe, so you should only need a few weeks to find your new apartment.
Getting an apartment is not just about filling out the application. It is also about making a good impression on the landlord. Dressing professionally, showing up on time, and being respectful during your meeting are all things that your landlord will likely be evaluating when they meet with you. Make a good impression, and you give your application a much better chance of acceptance.
Tempe has ample public transportation options. In addition to the Valley Metro bus service and the light rail line that the busses connect with, there are also two free shuttles that move through key neighborhoods, including downtown and the University. Bike lanes are almost everywhere, and the good weather encourages people to take advantage of them all year long.
The University is home to a number of museums and exhibits that are worth visiting, including the Museum of Geology. Shopping at Arizona Mills gives shoppers access to over 175 stores. For dining or a coffee, head to the Mill Avenue District. This is also where you'll find the bars, most of which are filled with college students. Pay a visit to Four Peaks to sample beer from the largest brewery in Arizona.