It is an incredibly difficult thing to come down firmly on the yes or no side of things. Hindsight can help especially as there is more information available - some of that information is only available because they did drop the bombs. On balance, looking at things from a time of (relative) peace I think I would have to side with no, they weren't justified. There is too much evidence that Japan would have surrendered without the need for the bombs.
However, to consider if they were justified, based on the information at the time, the situation America was in and the end of the war in Europe and Russia / USSR etc. Dropping the bombs was a horrific thing to do but war is horrific and it wasn't any more or less horrific than other acts carried out during the war. That doesn't excuse dropping the bombs but I have wondered if they are put under so much scrutiny due to the level of instant death and destruction. Sticking with Japan, was dropping the bombs actually worse than the fire bombings? in a sad reality, the answer is no. So to try and consider the question in context at the time, which is a far more difficult question to answer, I'd say yes that bombings were justified.