Haha, free time?
Third-years get little free time, they have to study to get into the university they want to enter. Even those who have failed and are not students but just preparing for entrance exams have little free time.
Second-years are not quite as busy with study, but more than likely have a part-time job to get them pocket money. They might get together and go to karaoke or something like that every once in a while.
First years are similar to first years, just with more time. Bowling, shopping, etc are usual.
Drinking isn't "rampant", it happens. High school students don't drink themselves into stupors or anything, but might get tipsy. Clubs and bars have been getting strict very recently, Japanese people without ID are being denied entry and sales of alcohol - foreigners generally aren't asked still.
All of the above are my own personal experiences over several years living in Japan, having studied in a Japanese high school, and still keeping tight ties to Japanese students both in high school and University, older and younger than 20 years old. Exceptions exist
Edit: Join a school club - my recommendations is something like tennis, basketball, soccer or a martial art. Avoid baseball or track and field as they are too serious and you will not benefit from it as well as you would doing other things.
Joining a club is the single best way socialise, make friends, practice Japanese, experience some culture and get better at something in Japan.