Not a TV drama, but the movie Uzumasa Limelight.
Kekkon Dekinai Otoko - I don't know if this is not popular, but I rarely see it mentioned. This drama won/nominated awards though. (There is a Korean version as well) One of my favorite Japanese dramas of all time.
Once Upon a time in High School - Korean movie about High School in 1978. This was actually my first Korean movie that I saw (and before ANY korean dramas). And I do not recommend it to be anyone's first experience of Korean movie or drama. Why? because I got confused, I saw this late in the 2000s, but the movie takes place in 1978. There were lots I did not understand at first. Like I didn't realize the main character was very good friends with the fat guy if it wasn't for that last scene lol. That said, I think it's a good movie.
Hello School Girl - Korean Movie about Older man and high school girl falling in love.
Fake Couple - Japanese drama based on...as you guessed it, Fake Marriage/couple. This is one of Amami Yuki's best work imo. You can really see the growth of her character in this drama (I don't really want to spoil but focus on her smile as the episodes go by). This is also one of Sawamura Ikki's most tolerable performance (for me anyway lol). It deals with other things as well, such as homosexuality, but not in a tacky way.
In the Mood for Love - Movie from 2000 by Wong Kar-Wai. Amazing cinematography and great script. This falls out of the "non-popular" criteria because it is popular to critics, film buffs, and other folks who are into movies. But for common/casual folks, I rarely see it mentioned.
Saigo Kara Nibanme no Koi - Seasons 1 and 2. This is basically a family drama in a nutshell. It has it's funny moments here and there and your usual touching moments as well. There is main romance between two older people, but it's a very slow burn romance. Here's the thing, the way the romance is depicted in this show between the main couple is very mellow. In fact, I expect people to get bored watching this drama. Why? because it isn't your usual romcom couple where they make a big scene or shout at each other or stare at each other, etc. The main couple talk....A LOT (the banter is one of the best imo). Heck I remember 1 scene where they talk for 10 minutes straight, no cuts (I maybe exaggerating), so be prepared for that.
Sexy Voice and Robo - another one of my favorite dramas. Great comedy and fun drama. Gets a bit serious near the end. Could've had multiple season but oh well. It's a bit slapstick in this comedy, but it really shows the range of the actors/actresses in this drama. This is definitely obscure imo.
Proud of Love - Chinese drama with the body swap premise. I just had fun watching the first season. Second season is alright I guess? Anyways, it's hilarious at many points. Of course, cliche moments are unavoidable but still the whole show is enjoyable. (This probably falls out of your "obscure" criteria.
The Pirates - What if I told you that there is a Korean movie about Pirates and Bandits? and that it had a high production value? Well that movie exists!