They weren't even really trying to surrender. They were given ample opportunity to do so. They were trying to vie for an armistice, cease-fire, or discussions (depending on when). That was not an option per the Potsdam Resolution. The only surrender that was to be accepted was complete and total surrender. We did, wisely, allow them to keep their Emperor (in name only) to ease the transition into a non-warring society with democracy, rights, and a representative government.
Had we not dropped the nukes, they still probably would have surrendered completely. It may have taken longer. A good documentary on this, if I can only recommend one, is Hirohito's War, it's an episode from Secrets of War. Had we invaded the main island, the loss of life would have been much higher, including the loss of civilian life. There are varied estimates as to how many lives such an invasion would have cost but none of those estimates are lower than the lives cost with the totality of both nukes and the resulting figures even due to shortened lives.
Frankly, as a whole, Japan got off pretty light compared to the number of civilian lives they took all across the area. If you compare their number of dead to those caused by them, they got off pretty light. If you compare them with the numbers of dead caused by their allies, the Axis, they really got off light. If you go back and read some of the documents printed, there were people who really wanted to kill each and every last one of them. Fortunately, nobody took any of them serious and those espousing such views were not in a position of power nor representatives of their governing bodies. Though, to be honest, judging by the number of atrocities committed and the scale on which they were done, it's not hard to understand the anger at the time.
Oh, I went and found that documentary if anyone wants to watch it. I believe that's one of the ones from the series that was narrated by none other than Moses himself. Here's a link if you want to watch it in your spare time:
There's something like 110 episodes or more? I don't remember how many. It's hours and hours and hours long. Some of them are actually really good and information density rates are nice and high. I've no recollection of any factual inaccuracies from the series but there's a few times where the facts are presented with biased emphasis and the take-away can be a bit skewed. I'm not sure if that's intentional but it's not uncommon - specifically where war is concerned. That's one of the reasons that I try to get my documentaries from multiple sources. Keeping bias in mind helps keep things in perspective. Most are not outright dishonest but may not include certain events that are important and salient. There's surely a limit to what can be included (due to budget and time constraints) but the attempt to color the findings in a certain light is not always unintentional, I think. So, use multiple sources from varied perspectives.