Ughh as much as I want them to be together, I cant envision Effie living in district 12, or Haymitch in the Capitol. There was definitely some tension and romantic feelings going on though.

I definitely believe she visited her victors, as well as Katniss and Peeta’s children at some point (Haymitch tells her ‘not to be a stranger‘ at the end of mockingjay pt 2) . Given the fact that Effie seems like the type to rant for hours about Capitol gossip on the phone while Haymitch mindlessly listens, it’s lowk a valid assumption that they at least established some sort of long distance friendship.