A Lull in the Ocean (depending on your tolerance for fantasy) or Planetes (depending on your tolerance for sci-fi) might be what you're looking for. Both are mostly concerned with the day-to-day romances between their main characters and the adventures that keep them apart (or bring them together), though I'd say A Lull in the Ocean leans more towards the slice-of-life you're looking for, whereas the characters in Planetes have jobs that are often a bit too exciting to fully be called slice-of-life. Full disclosure: I didn't especially like either, but largely because they're more what you're looking for, which is not what I'm typically looking for.