And now that we know some of the new mechanics in more dettail, some suggestions for already existing civs and their modified UA / UB:
India
UA: Land of the thousand Gods
You adopt the pantheon beliefs of every new religion that you encounter.
A way to show India's penchant for syncretic religion, its UA is set appart from Byzantium due to its focus on multiple small bonuses to its religion (pantheons) rather than on a couple of strong bonus (beliefs).
Arabia
UA: Trade caravans
Land trade routes have a +50% increased radious, religious preassure transmitted trought land trade routes gets doubled
By these couple of modifications, you can use your trade land routes as prime tools for religion expansion, giving them not only brute strenght (religious preassure) but increased reach as well. I think that this is a quite historical accurate type of UA, and that it promotes synergy between different types of gameplay mechanics and its UB, to boot (Bazaar doubles luxury resources thus making their trade routes more efficient).
Spain
UA: 7 cities of gold
Doubles the gold and happiness provided by natural wonders, natural wonder tiles yields +4 tourism
A small tweak to its UA, it still encourages exploration and setting near natural wonders while making it not too overpowered as it happened with their original UA (which could be a game decider) and tieing it with the new tourism mechanic to boot.
Egypt
UB: Burial tomb
+2 happiness, +50% to the chance of artifacts appearing near your cities
Your city yields twice the gold when invaded and one artifact to its conquerors
Because having a game that have introduced archeology for the first time in the series and it making no effects over Egypt or whatsoever simply does not make any sense. By increasing the chance of artifacts appearing near Egyptian cities you introduce a very late game bonus that rewards long term strategies (just like Pharaons used to think!), but making it as well a double edge sword, for that would make your lands far more attractive for pesky foreign relic-hunters, not to mention that it kind of, er, "synergizes" far too well with France's new UA, to boot.
America
UA: We the people
You can access ideologies with the discovery of the printing press, you can acquire ideological traits 25% cheaper
Earlier access to ideologies seems like a nice boost and make for funnier games, for it opens up more options earlier. The faster adquisition of ideological traits rounds up a trait aimed to make the US a powerhouse at the late game with a strenght based on its ideology and political system (which btw, is far more versatile for it helps every type of victory) rather than on culture or science per se, which seems like a more realistic depiction of the US (however, note that the two UU are still there

)
Japan
UA: Jade, mirror and sword (In reference to the 3 Imperial treasures)
Japanese cities are 50% more resistant to culture flipping, you recieve +3 culture on your capital for each different civilization that you have met yet you have closed borders with (note: CS's doesn't count, obviously)
A trait focused into the whole "culture as defence against influence" approach, Japan will be able to stand with its own ideology regardless of what the world thinks about it due to increased resistance against city flipping (less unhappiness created by pesky foreign influence) and its culture bonus from mantaining closed borders will provide it with a nice incentive to keep its borders closed that will disminish as the time passes (+3 culture is a massive boost on the early game, yet not so great on the latest stages of the game)