If you live in BR, you most likely are going to need a car. That's not to say that you won't be able to get around town without one, but our CATS bus system is terrible (unreliable and unsafe) and BR isn't bike friendly. Living near campus should be easier for those with a bike, but I'd still warn you to be very careful. We've had several bikers killed by people who were drunk driving or just not paying attention.
Yes, the traffic is bad especially after Hurricane Katrina uprooted so many people and thousands traveled to BR. But it is survivable if you allot enough time to deal with traffic. If someone says you can get somewhere in 10 minutes, allot at least 15 to 20 minutes depending on the time of day. It can't hurt to be early anyway
Also, our real estate is ridiculously expensive. I'm not sure how much the rental properties go for around LSU, but I know you should start looking ASAP.