The 2.7.0 #Mastodon update added a site directory feature. You can see it by adding "/explore" to your instance's address, for example:
It's opt-in, so it only lists people who have asked to be listed.
You can add yourself like this:
1. Go to Settings
2. Go to Edit Profile
3. Add hashtags to your profile bio, to let people know what kind of stuff you like to talk about
4. Tick the "List This Account on the directory" box
5. Click on "save changes"
mastodon.at is a microblogging site that federates with most instances on the Fediverse.