I can't say I ever remember this being brought up before, so I am kind of curious to hear people's thoughts about it.

I wonder what became of the invisibility cloak and the Marauders Map.

Personally, I believe Harry would keep the cloak for use in his Auror duties (and probably share with Ron as well when needed).

The map, on the other hand, is a little more difficult to determine it's fate. Could he have kept it to himself as a momento of both his adventures and as a tribute to his father? What about the possibility of saving it to pass down to one of his kids when they are older. If so, which one and why? Or (and I'm guessing this is really unlikely), perhaps donate to the school to help them keep track of the goings on within the castle walls?

While, I agreed that cloak stayed with Harry, I think that at some point it would end up in the hands of one of the children. I believe it was probably Albus. but that only speculation. As for the map, I think that Harry may have passed it on the Teddy. After all it was created by Remus as much as it was by James or Sirius. I also like to think that there was still a little of the marauder in the next generation.