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SourSteezleget the 35. 50 is great for interview type shots, but if you can find a lens that's 18-35, not sure if they have the sigma 18-35 1.8 for nikon (i think they do), but I use it on my crop cameras all the time and it's such a nice walk around lens for anything that isn't going to be a tight shot. 18-35 is such a nice range for crop, would highly recommend it
With all of this information in mind, please keep note of the lens format coverage. If the lens is designed for APS-C sized sensors, like your Nikon D5100, then you might want a lens closer to the 50mm range. Versus, if the lens is designed for full frame sensors, like on a Nikon D810, then you might want a lens closer to the 35mm range to compensate for that 1.5x crop factor on your D5100.
What other lenses do you own?
If you plan on sticking to the DX sized sensor for a while, invest in glass that is designed for APS-C sized sensors. If you plan on upgrading to a full frame sensor in the future, then invest in full frame glass.
There are plenty of options out there for Nikon mounted glass. Set your price range, and go see whats out there. If you are looking for a nice quality lens for half the price, I like to highly recommend Sigma.
I hope this information helped and that you get great coverage of your trip to Japan!
Well thanks for all the help - I went 35!