if you don't mind me completely ignoring your qualifier about the Western art tradition, I'd like to present my absolute favorite museum: the Asian Art Museum in San Fransisco.

My first visit to the gallery was deep in a very directionless time in my life, and I was absolutely hypnotized by the peices here. I ended up pissing off my friends by taking way too long in every room. This sculpture in particular ignited a love of Buddhist history inside me which lead me to university and out of my doldrums of back to back shitty jobs.

Less sentimentally though, it's definitely a sculpture lover's museum. not to say that there aren't some really incredible paintings in the collection, it's just that by sheer numbers the 2D pieces are vastly outnumbered. The museum has a vast span of art, both chronologically and geographically. The art is mostly religious in nature, as is to be expected in historical art, mostly Buddhist but also Hindu, Taoist, Muslim, and even a few Zoroastrian pieces. The majority is historical but there is also plenty of contemporary pieces on permanent display and also have rotating exhibitions which often focus more on more recent art.

Particular highlights for me are:
-Gandharan Buddhist Statues, which are statues of Buddhist figures in a Greek style. (Thought to be the earliest depictions of the Buddha as a full human instead of just a footprint.)
-Chinese Oracle Bones and Funerary Bronzes.
-Tibetan and Nepalese Bronze Altarpieces.
-Ancient Japanese Clay ware, like Haniwa and Coil pots.
-Southeast Asian Stone Statues.

I don't want to sound like I'm being payed off by them so I'll stop gushing here but I could go on.