... well, not a quite veteran but at 6+ DrupalCons, I know a few tips worth sharing.

TIP NO. 1 - THE PRENOTE

This is somehow a tradition of all DrupalCons. Before the actual Dries' keynote, you have the chance to attend an extremely funny show called "Prenote". The Prenotes are usually organized by Jam (Jeffrey McGuire) and Robert Douglas together with a group of volunteers. At DrupalCon New Orleans is on Tuesday at 8 o'clock and, believe me, you do not want to miss it. It's a musical, it has a plot, it is about Drupal and it involves Dries!
Check out the latest Prenote from DrupalCon Asia:

TIP NO. 2 - BOFS

DrupalCons and DrupalCamps have a more unusual and unofficial session track called the "Bird of Feathers". These are meetings/discussions of like-minded individuals who wish to discuss a certain topic without a pre-planned agenda. BOFs allow groups to meet and discuss issues relating to regular conference sessions and talk out common problems facing the community. It's the perfect place to have niche talks with a small group of people that share the same interests as you do. All ideas are good ideas and you won't get the chance to be bored, as they usually end after 15-30 minutes. All the ideas are listed usually on a board or in a special calendar on the DrupalCon website.

TIP NO. 3 - SOCIAL EVENTS AND EXHIBIT FLOOR

Besides the official schedule, all DrupalCons have many parties going on in locations near the event. 
Check the social calendar, ask around or if you visit the exhibit floor, some of the exhibitors of those parties will give your party invitations. My piece of advice is to be there at the agreed hour, as the free drinks won't last forever. Free drinks last until the budget is used and with such a large conference as Drupal, they do finish quickly so be there early if thirsty. 
Always be connected to your Facebook account and be sure to be following the #drupalcon hashtag to see where the crowd is going afterward. At the end of each day, you could also get a drink as some of the exhibitors have a beer hour. Another typical (secret) event it's the Whiskey BOF but I let you find what's that.

Hope this helped a bit and enjoy your DrupalCon!