SAO is what you'd call an isekai anime, which is a genre of anime in which someone from the normal world gets trapped or sent to another world whether it be through magic or technology gone haywire.
A very popular isekai anime that came out recently was Re:Zero. Really interesting show with a specific later episode that had an incredible cinematic quality it's something I would most definitely recommend to newcomers.
If you're interested in stuff where they get trapped in an MMO I would recommend Log Horizon, which I personally prefer over SAO due to it's realistic portrayal of MMORPGs and because it doesn't feature such a faultless one man army protagonist like Kirito (Not to say the protag in LH isn't powerful in his own right it's just masterful tacticians are more entertaining in my opinion.)
A more dark version and slightly different trapped in an MMO anime is Overlord. Different in that the protagonist is the only person from the real world and the MMO nature is downplayed and the show becomes more about the fantasy world and the protagonist's journey to world domination.
An even darker isekai anime is Hai to Gensou no Grimgar which isn't that isekai as no one can remember their past and it's only really hinted that they're from the regular world. Criticized for it's poor animation and it's pacing in which the main party has trouble killing goblins, I found something charming in it. A sort of realism of how most people would fair in a video-game-like fantasy world. In my opinion the worst thing about the show is its low budget which leads to occasionally shoddy animation and 4 minute long montages where an entire song is played(pretty sure they earned money by doing that), everything else in it is great in my opinion.
Speaking of fantasy, there's the anime No Game No Life featuring a pair of siblings who get transported to a world in which everything is decided with games. Total wish fulfillment and not objectively good but I enjoyed it and it definitely has striking visuals and a great soundtrack.
I've watched a bit of anime. But I think those are all pretty good places to continue from.
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