I’m going to have to recommend
Made in Abyss for sure. It’s an adventure anime and it has a bit of romance, but not to the point where it’s thrown in your face a lot or anything. It’s just hinted at and the story focuses more on the adventure. I believe there was a movie for the series recently too.
If you like stories that have to deal with life and how we handle it, plus one that has adventure, action, and a bit of romance, I’d definitely recommend
Fullmetal Alchemist: Brotherhood as well. It’s by Studio Bones, which is the same studio that produced
Soul Eater.
Then there’s
Hunter x Hunter (2011), which is undeniably one of the best anime out there and has a lot of adventuring in it. Albeit, it’s more focused on action, but it’s a really fun watch and you probably wouldn’t regret it.
Those are the main ones that come to mind at the moment. I’ll try to think of more along those genre lines. Let me know if any of these appeal to you though!