I'll be honest, I don't really listen to the music that's popular with my fellow Millennials and never really have. I've always been that guy who listens to classic rock and oldies despite not being from that generation.
But I will take a shot in the dark anyway and make a few predictions.
I could easily see some of the more "meme" type of popular songs being treasured in a manner similar to the pop one-hit wonders and novelty genres of the 60's and 70's (like how nobody remembers bubblegum pop as a genre, but everyone remembers the song "Sugar Sugar")
Examples of this would be songs like "Gangnam Style", "Call Me Maybe", "Tik Tok", stuff like that. Hell, I could even see widely hated meme songs like "What Does The Fox Say?" and "Friday" becoming part of the oldies stations' lineups when 2000's and 2010's music becomes old enough to be considered "classic", similar to how novelty songs like "Disco Duck" and "Surfin' Bird" are to oldies stations nowadays.
Lady Gaga will probably be remembered, especially for her earlier stuff like "Bad Romance", "Poker Face", "Born This Way", etc. In a lot of ways, Lady Gaga is to Millennials what Cher is to the Boomers or Madonna is to Generation X. Considering she liberally borrowed from both of their playbooks, I would not be surprised if she is remembered in a similar fashion as them (at least musically)
The edgelord mall rock acts of the 2000's like Linkin Park, Evanescence, My Chemical Romance, and the like are cringe-inducing now, but once the 2000's becomes a target for nostalgia, they will probably remembered fondly in a similar manner as a lot of the Goth bands from the 1980's and 1990's are today. The Cure and The Sisters of Mercy were ripe targets for snark back in the 90's, but are now fondly remembered by Gen X'ers looking back on their Goth years. I could see a similar thing with Linkin Park and the like, and as much as I hate to say this, I could easily see Amy Lee being compared to Siouxsie in retrospect by a lot of music and pop culture critics twenty or thirty years from now.