Much of how it might be considered hazing depends on how your risk managment documents are written. If it states "no scavenger hunts", any activity that can be construded as a scavenger hunt is in violation of your policy. Also verify with your universities policies. Some university policies are stated differently.

Something called a road ralley might be an option. As part of Engineer's week at my school the Engineer's Club hosts a road ralley. Its a pre-mapped route given by a series of clues with three check points. Its based on time to traverse and odemeter readings. Time is based on speed limits. The team closes to the correct odemeter reading and time wins. Teams dress up with themes for their car. It can be alot of fun and the last check point is a place for a cookout/party. Just ensure the rules obey your policies, including licienced and insured drivers and seat belts.