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I happen to be an expert on the topic of SoL:
I won't give my opinion on these, they are down to you to either like or dislike them.
SoL is a genre so vague that most people assign "slice of life/comedy" to a series that simply isn't action. This is misleading as the SoL element is actually a nondescript way to mark a series. Often the deciding factor is the tag that comes with it, and depending on what you like there are certainly many a good show for you. The majority of which have their own unique niche to fill, "SoL + X".
So you watched Azumanga? Great start, it's regarded as the foundation of most modern SoLs. What you liked about it will lead you onwards.
Did you like the sheer comedy value?
Then shows like Nichijou, Danshi Koukousei No Nichijou, Upotte, Pani Poni Dash, Joshiraku, Kill Me Baby, Ouran High-school Host Club, Kiniro Mosaic are for you. Very funny and very focused on being funny. The story lines are just bonuses.
Did you like the laid back atmosphere and casual normal school talking?
Then Yuyushiki (the king of friend talk), Yuru Yuri, Natsuiro Kiseki, Lucky Star, K-On, Hidermari Sketch, these are for you.
Now maybe these are a little too slice of life. You want something with some substance, a real story to it. That's fine.
Haruhi Suzamia, Beyond the Boundary, Tamako Market, Love, Chunibyo & Other Delusions, Hyokka, Kokoro Connect, (Air, Kanon, Clannad). Basically Kyoani is the studio for you! Oh and Girls Und Panzer, to a degree.
