I don't recommend petitioning at "high traffic places" - door-to-door with walking lists of registered voters with the required party affiliation is the way to go.
Too many people in "high traffic places" don't know where they live, if they're registered to vote, what planet they're on, etc. Those issues are reduced when you are at their doorstep.
It's quite common for people to crane their neck outside to read the house number off the front of their house - or ask me what street we're on... just imagine the validity of signatures from people who aren't at the location.
I also think it'd be useful if there ever were a court challenge to be able to testify that "each signature was witnessed at the address listed on the petition form" as opposed to testifying that "some guy at some Wal-Mart said he lived somewhere".
Republicans and Democrats can afford to waste time collecting bogus signatures. I can't.