From my perspective and in my experience (as a non-American citizen), American consulates are tightly guarded very unpleasant places where people often get mistreated.
As an American, you are less likely to be put through an awful experience, but I also find it very unlikely that it will be any fun. Note that much of the mistreatment I experienced was by local staff who abuse their position, not the Americans working there.
When you get there, you might expect very tall fences with sharp spikes and uniformed guards with machine guns. If it's in a crowded part of the city, there might not be room for tall fences, but the armed guards will be there.
At the consulate in Romania they won't let you pass in front of the building and will force you to cross the street. I am also aware of multiple occasions when they did not let people take any bags inside, no matter how small. They did not provide any place to safely store bags. Instead the (local) guard suggested that people should pay some of the taxi drivers idling nearby to keep the bags in the taxi's trunk. Now you can imagine that anyone who takes a mutliple-hour train ride to the capital city to apply for a visa at the consulate is going to have at least a small bag with their documents, wallet and phone in it; it's a necessity for such a trip. It's the sort of abuse of position I was referring to.
I am sure that American consulates are not quite as bad in all countries (though all of the ones I've seen from the outside looked menacing), but keep in mind that Romania is a safe country that is an ally of the USA and Romanians have typically pro-USA views.
Based on what I wrote above you can make your own judgement of how much fun it might be to visit one, even if you are an American citizen.