The tl;dr is “Yui x Ritsu”

The slightly longer story is that if you watch K-On! while really trying to overinterpret every interaction and assume more stuff is happening off-screen, a few romantic dynamics develop, with Yui x Ritsu being the most obvious.

The full story is 13+ charts and an 8 page writeup that I did as a personal project to justify this overinterpretation. I may post it somewhere if I ever decide to clean it up and make it presentable to the public eye, but there’s a lot in there. Ui x Nodoka. The Azusa->Yui->Ui and Jun->Mio->Azusa parallel. Yui-Mugi breakup arc. The Azusa human instrumentality arc.
My friends have called me schizophrenic for making these charts and while I don’t agree with their non-clinical use of the word “schizophrenic”, you should know that when I say “speculative / non-obvious” for K-On! in particular, it’s at about that level of extreme interpretation.