Hello. Welcome to the forums and to Lafayette
First off, there arent any real beaches in all of Louisiana to speak of. Its pretty much wetlands and mud flats up to the coast. The closest beaches are probably on the east texas shore or Mississippi gulf coast. There is one tiny "beach" in the southwest but it was ravaged by hurricane rita.
As for the nightlife, in my experience (which is limited since I lack much of a social life) it is centered around bars/restaurant hangouts, going to movies and a few clubs in town. There are a lot of fun festivals that stay open into the night and a lot of cinemas that stay open late. A lot of high schoolers hang out at the strip malls around Johnston street at coffee shops and the like.
Downtown is pretty nice to walk around in during the day but I havent really been there at night outside of a festival. There are a few clubs around like Grant Street Dance Hall that have live bands and the cajun music scene is of course prevalent. you can find several restaurants around town with live cajun music. The Cajun Heartland State fair is an annual fair at the Cajundome that is pretty good too. The Caboose is a little bar in town that my friends like to go to as well that is close to the university. Its a typical college town atmosphere you could say.
I hope this helped a little but I think others can tell you more in detail.
There is also an ice skating rink off of I49 that is really nice and stays open to about 9:00 pm.
edit: found a good informational site about Lafayette and Acadiana area events
CajunFun.com: Acadiana's Entertainment & Events Calender
The city is about 114,000 people and growing fairly rapidly. The entire surrounding area has about 500,000 people but a bit spread out amongst nearby cities and areas. Traffic is pretty bad but thats normal I guess. Overall it is a decent sized city with alot of fun-loving people who love to drink and party.