I am an older guy (you are way out of my range), but I will comment.
First of all, if you want men to approach you, going to bars and clubs would be a good idea. I am curious why you don't go. I don't know about younger men any more, but I don't generally approach strangers (men or women) in public unless there is a reason.
The key to meeting people is to go do interesting things with people. Do you have interests where there are single men? Do you go to meetups, or to church, or to a kickball league.
This is also the 21st century. You can initiate with men too. Find someone interesting and go an introduce yourself. Men are as insecure as women... and many cool men are nervous waling up to women. If you went and said 'hi' something great might happen.