Maybe a mod can merge this with the manga recommendations thread?
Yotsuba&! (slice of life, humor) comes to mind. I've only read a chapter or two, but it tends to be highly recommended by people here as a good clean manga. It's about a single dad raising his daughter.
If by "half-naked" you mean skimpy outfits, probably more shonen titles have skimpy outfits than shojo, so if you don't mind slice-of-life romance, then try Love so Life (romance plus some cute little kids), Lovely Complex (hilarious romcom), High School Debut (romcom), or Taiyou no Ie (romance). Or for fantasy romance, Akagami no Shirayuki Hime (woman wants to become a palace pharmacist), Ayakashi Hisen (ghost-buster style stuff with a super-nice male lead), Detarame Mousouryoku Opera (woman pulled into a fantasy world by a prince), and Ten no Ryuu Chi no Sakura (girl meets dragon). Also anything written by Midirokawa Yuki: Ayakashi Hisen (supernatural scool life romance), Atsui Hibi (short stories sometimes with a supernatural slant), Hotarubi no Mori e (more short stories), Hiiro no Isu (political fantasy romance, a personal favorite of mine), and Natsume's Book of Friends (supernatural story with a male lead, not particularly romance-focused).
Come to think of it, with shonen you might have more luck with more realistic genres like sports manga. For example, Cross Game (baseball) and Yowamushi Pedal (cycling) are both very clean. Cross Game has maybe one or two shots of a woman in her underwear (changing clothes) in all ten volumes, and that's it.