One of the easiest ways to get around downtown Lafayette and across to West lafayette is to catch the free trolley whcih does a circuit around points of interest. You can hop off and on at set stops to your hearts content.
You can catch this ride at any of the stops which are well signposted, there are also maps available for the trolley route from a lot of the stores in downtown Lafayette. The trolley will take you to neighbouring West Lafayette and onto the Purdue campus. We did this one day just to see where it took us. We were impressed with the trip, the trolleys and the route. You could get to a lot of the "must sees" from this route. Certainly a painless way to travel around Lafayette. I would recommend this to anyone who wanted to get their bearings in the area.
You can either fly into Purdue Airport in West Lafayette, or fly into Indy or Chicago and drive. Or just drive from wherever you are. ;) Likewise, greyhound serves the area and Amtrak has a twice-a-day stop here (once going north and once going south).
Car, bus, taxi... you might be able to ride a bike, but I wouldn't reccommend it.