I join the others in saying that you have made it difficult to yourself to get that reimbursed. The norm is to ask the airline to provide you with accommodation (they are obliged to) and indeed, if they refuse you would have a very strong case to book your own and get reimbursed.

However, in this case, you asked at the transfer counter, they told you where to go, and when you say you could not find it you went on and booked your own. I think this is going to be considered a very thin excuse. First of all, unless it has changed very recently, the place where they take care of accommodation is really quite easy to find, and second, even if you did not, in KLM's own hub, you could have asked any information desk or any KLM agent who would have reexplained to you where to find the place.

My guess is that since, as you say, you did not "trust them to book [you] somewhere nice and close to the airport", you did not try very hard thinking that you would be better off in a place of your choosing. Unfortunately, this is a case where there is a clear alternative between them paying and you choosing and you can't have the best of both worlds. Their EU261/2004 obligations involve providing you with food and accommodation, not providing you with nice food, nice accommodation, or accommodation close to the airport. Moreover, if you had gone to the counter and they had put you up in a prostitutes hotel 80 miles away from AMS, then you would certainly have had ground to complain, but in this case, it was simply your guess that the solution you would be proposed would not be your favourite. This is simply not going to cut it.

So you can contact KL and explain them the situation, but from my understanding you have absolutely no right here (you surrendered it when you decided to go for your own accommodation plan) so the only way you can really ask it is as a gesture of good will.