There's a famous quote by John Phillip Sousa that goes:

These talking machines are going to ruin artistic development of music in this country. When I was a boy, in front of every house in the summer evenings, you would find young people together singing the songs of the day, or the old songs. Today, you hear these infernal machines going night and day. We will not have a vocal chord left.

(Not the best source, but here's a source anyway)

JPS was born in 1854, so he would have been in his teens/twenties around the period you are describing. Vinyl records weren't popularized until (I believe) the early 1900's, so although I don't have a date for the quoted statement, I think it's safe to assume that it was made several decades after the period you are asking about. If JPS is to be believed, singing in groups may have been a common activity for youths around that period.

Of course, his opinion (maybe even his childhood?) was extremely biased and perhaps this quote shouldn't be trusted, as he was trying to make an argument against the popularization of recorded music and may have been speaking in hyperbole or just remembering his own childhood through rose-colored glasses.

EDIT: /u/xmachina provided a source dating the JPS quote at 1906.

At a job previous to the one I have now, I transcribed the 1879 diary of Florence Ranger, a young woman of Glens Falls, NY. The object listing is here, and it contains a link to read the full transcription on Scribd. Florence was upper middle class and documented her time pretty well - what she read, her social engagements, etc.

Stephen DeForest Hopkins's diary of 1858 (sorry, slightly earlier than your requested time period) is similar, although he spent a ton of time pining over his future wife as well as noting that he played backgammon and walked to the post office.

I'm currently sitting at work with several "Godey's Lady's Books" in my hands, but unfortunately I work at an antebellum house museum so my hard copies cut off at 1859. However, they are digitized in many places, I think even Project Gutenberg, and also here.

Godey's was the lifestyle magazine of its day. In it you find songs, fashions, recipes, etiquette, home remedies and even short stories by notable authors. It is invaluable in learning about women in the time period, and though you are asking about teens, the etiquette and fashion and flower language would definitely apply to them. I'd say it was more upper-class, but a middle class family yearning for higher status would read it too. So if you're looking for how marriageable youths entertained themselves, danced, sang, and dressed, I would check there if you have spare time. When I'm off work I could maybe do some of that research for you.

Louisa May Alcott wrote a number of "coming of age" novels in the time period you're looking at (Little Women, Little Men, Jo's Boys, Eight Cousins, Rose in Bloom, and others). While her novels are, of course, fictional, she depicted the life she knew and should give you some idea as to how young adults spent their time in that era.

Anyone have details on the bicycle fad of the late 1800s?

I read a bit about it a long time ago. I remember there was something of a moral panic, since young men and women used them for dating without a chaperone, but my memory on the subject is sketchy.