If it's the 80s, the big two of romance were Maison Ikkoku and Kimagure Orange Road, back when "fansub" meant getting an
nth generation VHS tape via mail order with the subtitles spliced in. Both are somewhat archetypal "love triangle" romantic comedies, especially since they were about as influential in the genre as Sailor Moon and Studio Pierrot's works were in magical girl series, but by the same token, they avoid some of the pitfalls of that the staid retreads of the genre have done since because they aren't blindly following anime genre conventions (which didn't really exist yet).
Kimagure Orange Road is about a son in a family of espers (telekinetic, teleperception, teleportation, along with some other powers), who must keep their powers secret, but since he and especially his younger twin sisters tend to have trouble with that restriction, they tend to have to move quite often. After one such transfer, he ends up falling in love with local "delinquent" Madoka, but runs into issues when Madoka's best friend, Hikaru falls in love with him. A lot of the episodes tend to focus on the wacky hijinks and misunderstandings that ensue as he tries to keep his powers secret on top of the usual love triangle shenanigans and so forth, but quite a few episodes are genuinely sweet as well. The first movie is also probably noteworthy for noting just what happens when you lead someone on for quite some time before unceremoniously dropping them for their best friend.
Maison Ikkoku about a student ronin (in the modern sense - someone who has graduated from high school but hasn't passed their college entrance exams; I suppose they'd nowadays be called NEETs) named Yusaku Godai who lives in the titular boarding house and falls in love with the new manager, Kyoko Otonashi, who herself recently came to Maison Ikkoku due to some recent heartbreak. Twin love triangles end up forming, each centered on Godai and Kyoko. It's a Rumiko Takahashi work, so there's also an ensemble of eclectic side characters (who mostly tease Godai for their own amusement, though they do get shots in at each other and Kyoko as well), but the focus is on the main two characters. Godai actually grows as a person throughout the series, as does Kyoko; the usual "comedic misunderstanding" trope that you see so often today is unabashedly used and abused, then preemptively deconstructed in the last few episodes. Also, arguably one of only two Rumiko Takahashi works that actually has a proper ending (and a really good ending, no less; she should do it more often).
Honestly, I never really got into Kimagure Orange Road nearly as much as I did Maison Ikkoku - it probably was in part because KOR was unabashedly magical realism while Maison Ikkoku is pure realism (except Yotsuya...he's just odd). The biggest problem is that neither can be qualified as short - Kimagure Orange Road is the shorter at 48 episodes, 8 OVAs, and two movies, while Maison Ikkoku, as is ordinary for Rumiko Takahashi, clocks in at 96(!) episodes. If you want to put the time investment into that, I'd also suggest Legend of Galactic Heroes, as Haspen almost said.
Also, this conversation is seriously inspiring to go track down some of the really old recommendations I never picked up, like Patlabor. Other mentioned stuff: Rose of Versailles is indeed very, very awesome historical fiction, but clocks in at 40 episodes. Hmmm, out of the specified timeframe, I can think of a few more. With Cowboy Bebop mentioned, Trigun always used to always be mentioned in the same breath as another Western-styled sci-fi series, though I don't hear as much about it nowadays. For police comedy, You're Under Arrest tends to come up, and sci-fi comedy of the 80s and 90s can't really go without mentioning Irresponsible Captain Tylor. I liked the movie Wings of Honneamise quite a bit, except for
that one scene which seemed to come out of nowhere. The original Japanese release of Macross is actually in time-frame, convenient to list alongside Mospeada, and was really good, just as Reelya implies (and at 36 episodes, it's not too long compared to some of the others). Lodoss Wars and Patlabor are names that come up often; 3x3 Eyes, Battle Angel, and Key the Metal Idol somewhat more infrequently. Unfortunately, though, I've seen quite a few of these, but looking them up, those three seem to at least be short - OVA length, and not "Legend of Galactic Heroes" OVA.