A socially awkward author from New York City only leaves his apartment at night until he falls in love with an ambitious politician who is spending every day in front of a camera.

I suggest you increase the psychological problem the author has, right now he comes across as uncomfortable in public - no biggie.
What if he was an agoraphobe? What if he has a meltdown when in public during the day. Simply being socially awkward could describe a large portion of the population, and likely present a lesser obstacle than agoraphobia or something similar.

Very interesting combination. Somehow I am thinking of?Notting Hill.
I like your original version. I think that your second version includes the stake (by the way, moving to another city seems acceptable), while the first version works better for me as a clear nice hook.

Good advice above.

Most good romcoms have a plot device, story element or character that provides the MC with an obstacle for being with their one true love. I feel like this concept needs something or someone keeping the author from pursuing the relationship. Bit cliche' but what if the politician was engaged to a douche bag?
Or his or her parents are against the politician being in a relationship with the author?
Or the politician is sent to a far away place and the author must travel to be with him or her?