I lived in East Lansing for two years without a car. You can move around campus either by walking, riding a bus, or biking. If you dont want to have a car, live in apartments that have access to line 1 CATA bus, which runs every 10 minutes. I found other bus lines are just too slow to be reliable. I'd suggest you to get a bike if you dont want a car. Apartments in these areas are nice: east grand river, oakridge avenue, coolidge rd, northwind drive (ok-ish), etc
I moved from East Lansing six years ago, hopefully things dont change that much.