re: Where can I park coming from the Northshore?

Get off the interstate at Tulane. Come down to the area around the LSU Health Science Center, which is right around the old church. Park on the street in this area.
If those are all full, just park on Tulane facing back toward interstate.

This is for free easy parking if you aren't going to want to bar hop and such.
If you want to hit up the warehouse district, you can find pay lots and such on that side of the dome.