I am myself a big fan of comedy & slice of life so I have a few recommendations. If you do watch any of them I'd be interested to know how you liked it. :)
Comedy & Slice of Life:
Comedy, Slice of Life & Romance:
These are just off the top of my head if you want more let me know I'll have a look through my watch list.
+1 Gekkan Shoujo Nozaki-kun +1 Wotaku ni Koi wa Muzukashii Barakamon Gakuen Babysitters Hinamatsuri Karakai Jouzu no Takagi-san Miira no Kaikata Saiki Kusuo no Psi-nan
Kimi No Todoke is a cute romantic one with a unique art style, and although I haven’t seen it myself, my friends all insist that My Love Story!! is fantastic and adorable. I’m personally a big fan of Kaichou wa Maid-Sama and Kamisama Hajimemashite. If you’re up for some manga reading, Denkgeki Daisy and Skip Beat (which I think has an anime? I haven’t watched it) are both super cute
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Gekkan Shoujo Nozaki-kun and Wotaku ni Koi wa Muzukashii are both delightful. Horiyama is another great slice of life anime, and episodes are coming out weekly on Hulu. I read the manga a few years ago, and it's one of my favorites.

Gekkan Shoujo Nozaki-kun is AMAZING for comedy haha but not all pure romance watchers enjoy it since it focuses more on comedy! :D Let's see here...
for comedy: Saiki Kusuo no Psi-nan is seconded!! Barakamon is also veryy good Tanaka-kun wa Itsumo Kedaruge for sure Shirokuma Cafe! Also slice of life! Non non biyori? Osomatsu-san and its many seasons - this one mightt be up your alley because... there is definitely Gintama too, but be warned as there is toilet humor for both of these!
for slice of life: Mushishi is a definite but it is on the sad side Natsume Yuujinchou! Tsuritama is a good one Omoide Poroporo is a calm SoL! Uchuu Kyoudai Kobayashi-san Chi no Maid Dragon Beck and Eve no Jikan are recommended as well! Hanasaku Iroha
with romance, also seconding Kimi ni Todoke AND Ore Monogatari/My Love Story! For the former, Sawako is very much one of the best characters ever she's great! Wotakoi/Wotaku ni Koi is if you want a romance but in a workplace setting with adults!
few more romance options: Tsurezure Children Akagami no Shirayuki-hime Toradora From Up on Poppy Hill Tamako Market
kamisama kiss is one I just watched! maybe I'm a little late but I loved it sm
Gekkan-shoujo Nozaki-kun is really funny, I agree. I also recommend Senryuu Girl, Acchi Kocchi and Teasing Master Takagi-san.
Toradora is a good shoujo anime. The World God Only Knows is good too, though it gets somewhat serious at the end.
I haven't read a lot of shoujo recently, so I can't really remember a lot off the top of my head.