The summer is a good time to look for an apartment in Tulsa. May is a good time to start your search, and you shouldn't try looking for an apartment any later than the end of July if you want good results. Remember that the closer it gets towards fall and winter, the fewer options you're likely to have.
Don't delay getting your applications into apartments that you're interested in. All other things being equal, some landlords will deal with people on what amounts to a first come first served basis. If you're interested in an apartment, be prepared to try and pull the trigger on it immediately, otherwise you risk missing out.
Tulsa is a very bike friendly city, with a very large independent bike trail system. These paths also connect to the Universities, making biking a great way for students to commute. Tulsa Transit operates busses in Tulsa proper and to the suburbs, but service to the suburbs is sporadic. There is also a very good series of highways that make getting around by car quite convenient as well.
Tulsa's museums and art galleries preserve a rich cultural legacy for the town. The Oklahoma Jazz Hall of Fame also frequently features great performances. For high-end shopping, head to Utica Square. For a blast-from-the-past experience, try the Max Retropub. This bar features videogames and arcade attractions that were made popular back in the early 90s.