Once you get into searching for phones with wide LTE band compatibility, the price goes up.
http://en.wikipedia.org/wiki/List_of_LTE_networks
From the sticky on pre paid sims, pre paid LTE around the world
http://www.flyertalk.com/forum/trave...und-world.html

In Japan, you'd need to rent an LTE sim from jcrcorp.com if you wanted full LTE speeds as the prepaid data MVNO data only sims only offer throttled LTE (which is no faster than a halfway decent 4G HSPA+ connection). You'd also want to rent or roam if you want voice as there are resident restrictions to purchase voice/voice+data sims.

The Sony Xperia Z Ultra c6833 has pentaband UMTS and supports 8 bands of LTE including 3, 7 which is in use in Germany and Singapore.
http://www.gsmarena.com/sony_xperia_z_ultra-5540.php
Sony Xperia Z2 also has a model with pentaband UMTS and 9 bands of LTE. It is a new model and therefore likely on the pricier side.
http://www.gsmarena.com/sony_xperia_z2-6144.php

Sony phones usually have less custom rom development activity than Nexus or Samsung. Build quality on the flagship models is nice, though.

The Nexus 5 North American version can be used on Sprint MVNO Ting, if you're only looking to carry one phone. For $150, an unlocked Moto G GSM is a good option as a second phone for travel. You won't need to pay several months service, early termination, or unlocking fee. The dual sim version is a bit pricier but also provides a few more options, including domestic. It can work on sim using AT&T in one slot and T-Mobile in the other.