For classical tourism locations, you might be having troubles since people of that age do not really like to travel to temples and other places that tourists like.
Younger Japanese people prefer to go abroad (Korea, Hong Kong, Thailand) since this is often cheaper than traveling in Hong Kong. And since they have to go to Japanese temples and museums with the schools, they are rather happy not to have to do that once they have a choice.
If you want to meet young people, nightlife is surely the better solution, no matter where. On the other hand, you might want to consider locations like Tokyo Disneyland or Disney Sea Land, since those also attract a lot of different aged people.
Another option that I can highly recommend is going to Matsuris, concerts and fireworks, specially now that summer is approaching. Why?
- Matsuris happen frequently and are often used by younger people to dress up and meet. They normally last one day or a weekend and allow you to interact with people. You will of course also meet families with kids, but still have a fair share of younger people. Many temples have one day in the year where they organize one, and often block off some smaller street from the traffic where then small games are setup for people to (pay and) play. While there are much bigger ones, the smaller ones will allow you more to meet people who live around the corner.
- Fireworks in Japan, specially in Tokyo can be a huge event where more people show up than you would care to count (approaching a million). For the ones in Tokyo Bay, you will likely see the largest amount of people outside a stadium ever in your life. But since people go there early to find a spot to see the fireworks, stand around, drink beer and eat street food for hours, they present a perfect opportunity to walk around until you meet a friendly group you can share a beer with. The biggest difference from the Matsuri is that people come from further away, and whomever you meet might not be able to stay in touch with you.
- Concerts are great to meet people for all the obvious reasons, same as everywhere else in the world. If you get to show that you like Japanese music, you show your interest in the local culture and will most likely not meet a lot of other foreigners.
One more option to mention are general hangout-spots like parks, open-air restaurants and bars etc. Since Japan after all is a crowded place, wherever you go will give you options to sit close to people without coming over creepy and get to talk to people. I personally found that just sitting at a sushi-counter is a great place to start conversations with the chef and in return also with the people sitting next to you.