somehow I really want to recommend How I Met Your Mother, because it fits your description
so perfectly, but since that is a "US drama" ... for the asian ones, maybe Taiga ("epic") Dramas are worth checking out.
They are usually rather long, about 50 episodes, and from the ones I've seen mostly maintain a certain level of high quality story and acting. Content-wise some may be more interesting than others, depending on your tastes ... in general the more recent ones are easier to find online (and with good video quality).
For romance, probably those staring female main characters are good, like
Gou or
Atsuhime ... or maybe
Komyo ga tsuji ... but well, there are like more than 50 different Taiga dramas ... so just try some ^^
Apart from that there are the different "Condor Heroes" series, which are also pretty long.