I'm currently playing Research Story, that one is pretty cute. There are romances. I don't know about combat since I haven't gotten that far (just a few hours of play); it doesn't really seem like there will be combat, but there could be.
I'd also recommend Apico, Mudborne, Littlewood, or Fields of Mistria. I'm sure I'm missing a ton. I think Steam has "Cute," "Romance," and "Slice of Life" tags if you wanted to browse those on the storefront.