I always have trouble separating between Magical Realism, Surreal series with a relaxed tone/present-day setting (Shimeji Simulation, Dainana Joshikai Hokou) and otherwise realistic series with a surreal style (Oyasumi Punpun). Hopefully these fit the bill for you.
SoreMachi - Often lapses into Magical Realism, but always remains first and foremost a SoL focused on a neighborhood. Even if the situations can get outlandish and the tone isn't necessarily serious, there's a lot of care and attention to some of the characters and their dynamics. As a result it often feels quite "real" regardless of the chapter's plot. Big favorite of mine.
Scientia - Short story anthology that takes scifi concepts that are usually portrayed as negative and gives them a more sympathetic look. Not quite magical, but has an otherwise grounded tone close to the genre.
Babel no Toshokan and
Mikake no Nijuusei - Two magical realism stories by Tsubana. Quite different in tone and subject-matter, but both share the author's blunt, "matter of fact" storytelling style.
Dead Demon's Dededededestruction - It's an Asano manga, so if you've read his stuff before you'll probably know what to expect from his style. This one leans a bit more on the supernatural elements.