General

[b]Akatsuki no Yona[/b]
Amazing manga so far. Now that it has an Anime it has picked up the pace in getting releases as well. Main character is incredible as opposed to most adventure/romance girls.

[b]Fushigi Yuugi[/b]
It's a bit of an old one but I think anyone who likes Inuyasha has watched or read this at some point. It's good. Watase Yuu has a lot of similar adventure/romance mangas. I also recommend Alice 19th and Ceres: CElestial Legend if you like Fuushigi Yuugi.

[b]Kamisama HajimemashXte (X = i )[/b]
Incredibly similar to Inuyasha with basic plot details. I won't say too much because that will involve spoilers, but I definitely think it's worth a read. It is a bit more lighthearted than Inuyasha though.

[b]Hanasakeru Seishounen[/b]
It's been a while but I watched the anime to this. I enjoyed it. Not sure if it had a lot of adventure in it though.

[b]Tsubasa Reservoir Chronicle[/b]
One of the most confusing mangas I have ever read by CLAMP.

[b]Katanagatari[/b]
It's an anime I suggest you actually watch. I know it's not a manga and all but the OST and art are both amazing. It has a lot of adventure and not too much romance, but it's nice and subtle. Sorry about the ending in advance.

[b]Ramna 1/2[/b]
It's a high school setting, so it's less adventure based. Although there's definitely parts in the manga that qualify for that genre. It's also by Rumiko Takahashi so right up your lane.

[b]Kyoukai no Rinne[/b]
The romance progresses slow as hell but again it's by Rumiko Takahashi. Also has a high school setting but it features more paranormal things.

[b]Rurouni Kenshin [/b]
The romance isn't exactly something that progresses immensly but it's worth a read and watch.

[b]Akagami no Shirayukihime Manga[/b]
I really love the costume art in this. The adventure part comes later in the manga but it's a good one.

[b]Sailor moon[/b]
Nice and simple. It's the mother of all shoujo. The manga is tons better than both the anime. It's got a lot of romance and a decent amount of adventure.

[b]Bride of the Water God[/b]
I keep dropping this one personally because it doesn't get updated as frequently (maybe it's already even done?), but it's a lovely manga.

[b]Some that I just don't remember or don't completely fit your criteria[/b]
Saiunkoku Monogatari
Otome Youkai Zakuro
Tenkuu no Escaflowne
Full metal panic (I liked this a lot actually)

Tsuyokute New Saga definitely give this a read.

You want to try the light novel Mushoku Tensei instead? I usually just put an epub version on my phone for long commutes.

Immortal Rain
Kekkon Yubiwa Monogatari
Tsuyokute New Saga
Tate no Yuusha no Nariagari
Hoshi no Samidare