Birmingham seems silly, and not because of the politics of Alabama. The location of a convention has little effect on the final vote tally. Problem is logistics. Last cycle's Democratic convention in Charlotte was a bit of a clusterfuck, with hotels up to 50 miles away booked solid. And that's a city with a population of 775,000. Birmingham has a population of 212,000. No way they have the facilities to host a major party convention. (Also, not a single unionized hotel.)
Brooklyn has everything a convention needs, and it's convenient to the center of the US media world. Politically, it brings nothing, but like I said above, no place does. Logistically, well, it's New York. The biggest downside would be cost, because that's one expensive-ass city.
Cleveland is the site of the Republican National Convention. Logistically, it might be the easiest place to host the convention, because Cleveland will already be working to implement many of the security and support services the Dems will need. Some think that the RNC's choice knocks them out of the running, but I don't see why that should be the case. A Battle of the Bands-style convention season would be fun.
Columbus is such a low-key city that I have zero sense of their logistical capacity to host a convention this size. But it is surprisingly the largest city in Ohio with a population of over 800,000 (Cleveland is at around 400,000, Cincinnati around 300,000).
Philadelphia is in a swing state (if that matters, which it doesn't), has the logistical capacity to handle anything, isn't as expensive as New York, and is central to our nation's historical heritage. Wouldn't be a bad place to nominate our first woman president.
And then there's Phoenix, and unless Democrats want to stir up the same raw emotions and divisiveness that Netroots Nation did with their choice for that locale, it should be avoided like the plague.
With the exception of Birmingham, which is an odd addition to the list, the other four cities would unite our party and allow us to focus on the task at hand—retaining the White House, expanding our Senate majority and taking back the House. Let's focus on the places that unite us, not consider places that divide.