Well, I think @joannalannister and others have correctly called it that there would be a Golden Sept in Lannisport. (I’m imagining the walls and ceiling in gold mosiacs like St Marco’s in Venice with tons of candles to make the whole thing but larger-than-life grandiose statues in full-blown Baroque style, like Bernini but in gilded bronze)
The Vale’s Sept would probably be called the First Sept or something like that to emphasize their love of tradition and ancestry – given the Vale’s marble industry, the whole things going to be in gleaming white marble and quite grand but austere, with the main feature being huge statues of each of the seven in different colored marble. I’m also guessing that because of when the whole thing would have been built, the Warrior and the Father would be most prominent.
Similarly, I’d guess that the Stormland’s Sept would be made all in glorious, gleaming polished hardwoods and have beautifully carved wooden statues of the gods. I’m guessing the Smith is probably depicted as a woodcarver or lumberjack. So maybe looking like Russian Orthodox Churches made of wooden with onion domes and the like?
Dorne’s Sept would have to be rather unusual, given the ways that their Rhoynish culture clashes with the Faith’s normal attitudes about gender roles, sexuality, and so on and so forth. So I’m guessing hardcore Marianism, but with more of a focus on fertility and sexuality, and also a bunch of former Rhoynish gods reinterpreted as saints and the like. Basically I think of some of the more colorful Hindu temples.