Know-How Exchange : Advertising/PR

Presumably your (internal) goal of your concert is to collect contact information of people interested in your concert for ongoing marketing efforts. Secondarily, it might be a good idea to determine which of your marketing efforts yield the best results. Therefore, I suggest each of your marketing efforts take the content entrants to a separate landing page which you can then measure with website analytics.

As for "what" the contest prize is - that depends on the performers and venue. You could have a private concert for the winner & his friends. A VIP backstage party/reception with the band. Travel with the band to another concert venue.

For the contest is - that should depend on your goals: who are you trying to get to enter (age/demographics) and what that group care about (money, status, friendship, etc.). The prize(s) need to be amazing enough to interest people (and their friends) to enter.

Oh - and don't forget social media marketing - Facebook, Twitter, etc.

The above comments nailed many aspects very well.
For a contest theme, breaking away from the basic "name that tune" how about a contest where people can revisit their past when they went to a concert, etc. Get them to submit their best or craziest concert picture or story. They may engage more if they can relive their past. And yes, offer great prizes.