If you want to find a place in Lubbock, you need to start looking early. The appeal of Texas Tech means that many new people are moving to town both to study and work each year. January and February aren't really too early to look, but by the end of March you definitely want to be hunting for a place.
Don't wait to hear back from your first choice apartment before you schedule more appointments. You want to have backups in case you end up not getting in at your first apartment, and if you wait too long, you could end up having to take accommodations somewhere far from your ideal location, as good spots get snapped up quickly.
Unless you plan on coming to Lubbock with a car, use the bus routes to help plan your apartment search. The primary bus routes all either visit the university or connect to other routes that do. A nearby bus stop can make living anywhere in the city convenient.
For people new to town, the local monuments to Lubbock's history can prove entertaining for many months after you relocate. Not to be missed for music fans is the Buddy Holly Center. The city is also home to a number of festivals that run from April until September, featuring everything from the arts to cowboys. To really get in the Lubbock spirit, take in a Texas Tech Red Raiders game.