I was meaning to ask this a while back, so here goes! I think Touhou's themes are too broad and complex to capture in a single character, but anyways here goes. Touhou broadly covers several central themes:
Dreams/Fantasy vs Reality/ScienceIf I had to pick the singular central theme in Touhou, this would be it. The world of Touhou is literally called the land of fantasy, after all, and the border that separates it from our world is both a physical one and a ideological barrier. In Gensokyo, fantastical is the norm, while in our world, we live in a scientific age where belief in fantastical things such as youkai is at an all-time low.
The sort of dreamy "is this fantasy or reality" trope is touched upon many times in the series, most notably in the lyrics of Innocent Treasures, which directly references the story of
Zhuangzi and the Butterfly. The music CD's in general lean much more heavily into this theme, as they follow around the future Hifuu Club, which lives in a dystopian future where children don't smile and natural bamboo no longer grows. There, the harsh, advanced, and scientific reality is contrasted sharply with the fantastical, dreamy, yet unforgiving land of fantasy, Gensokyo. I would really recommend reading all the CD stories as it's some of my favorite worldbuilding and writing from ZUN.
Nostalgia, Culture, and FaithRelatedly, Touhou as a whole is heavily driven by nostalgia and respect for "outdated" culture. ZUN famously declared EoSD "A 20th century shmup for the 21st century", and was his way of channeling his love for shmups, which even at the time were already starting to decline in popularity.
He loves respecting tradition and doesn't always believe that the modern or scientific way of doing things is the best way.
Gods, traditions, and legends, all cast away by our scientific age, find a new home in Gensokyo, as long as they have believers and thus faith.
The whole "faith" idea (that gods and beings in Gensokyo derive their life force from people's faith in them) is a pretty interesting concept introduced in MoF. It's sort of a meta-thing too, in that ZUN brings awareness to old and forgotten gods, legends, and stories through his works, thus increasing their faith and giving them a sort of "second life" in our world.
Acceptance and Social OrderAs mentioned by Cyber, another theme in Gensokyo is that it is all-accepting. Major troublemakers settle down and just join in on regular life after their incident/game is over. What's interesting about this though is that Gensokyo is actually bound by a pretty strict social order where everyone has a role to play -- youkai and humans have a special relationship where humans actually supply youkai with the faith necessary to keep them alive, and humans native to Gensokyo are actually off-limits to the youkai. The protagonists (mostly Reimu) are the ones responsible for resolving youkai disturbances, and all battles are bound by the honor system of rules that is the Spell Card Contract.
Kind of rambly and not what you were looking for but that's my thoughts.