My recommendation are:
Kimi no Na wa
Koe no Katachi
Shigatsu wa Kimi no Uso (extremly my favourite)
You've probably already seen it but try Seiren, not as good as Amagami SS but follows the same style and its shorter.
OMG Plastic Memories and Say I love you!
My personal favorite (as a straight man) is a yaoi, believe it or not. I think it's called sekai ichi hatsukoi. Only yaoi i've watched but it was the best romance i've seen.
A silent voice is pretty good romance movie
hmm i remember one called true tears that i liked at the time. but i don't remember it very well anyways it should be good!
boku no pico ;)
Plastic Memories now said twice because it's really good, Sakurasou no pet na kanjo, and Toradora!
Lovely Complex is pretty good. There is no fan service in this show (bummer amirite), but it makes up for it with chemistry of the two main characters.
TSUKI GA KEREI~!