Detroit is very culturally diverse, which gives the city a unique atmosphere. There are little cultural districts and neighborhoods all over, like Greektown and Mexicantown. There are also tons of things to do around Wayne State University. There is Campus Martius Park, Detroit Institute of Arts (DIA), Greektown, sporting events, Belle Isle, Detroit Opera House, Fox Theatre, and the Detroit Science Center, just to name a few. You can even cross the border into Canada to go to the casinos! If you don't want to do any of the things just mentioned, there are always student organizations on campus looking for new members and volunteers for projects/events.
Detroit is a city and cities have crime, so you will need to use common sense to judge the areas you need to avoid. But Detroit is trying to clean itself up and make it a safer place for people to visit, and it is definitely paying off. There are some other colleges near WSU, like the College for Creative Studies, which is within walking distance, but others require a car to get to, such as Eastern Michigan University, University of Michigan (Ann Arbor and Dearborn), Marygrove College, and a couple others. A few WSU students know some people at these other universities and will get together, but interaction between the general student bodies does not happen much. Overall, Detroit has a lot going on, but it is up to you to make use of all the opportunities.