I kind of thought that the new Red/Blue battle theme in these games sounded like Zinnia's. It's a nice mixture of old and new sounds at least.
Battle and character themes aside, there were a few tunes that caught my attention.
Maile City and Vast Poni Canyon have some nice tunes. I love Japanese style music so Malie City was a plus and Vasi Poni Canyon has such a catchy theme; gives a feeling of adventure. The Tapu Ruins and Ultra Space themes are pretty cool as well, it really gives the right feeling for the areas.
I've come to like the Akala routes music, the Island Kahuna battle music, the standard trainer battle music, the festival Plaza main song, the music that plays when you're inside a clothing store, Hau'oli City daytime, and the Victory Road equivalent.
Maile City and Vast Poni Canyon have some nice tunes. I love Japanese style music so Malie City was a plus and Vasi Poni Canyon has such a catchy theme; gives a feeling of adventure.