I think you're both right
I would have liked a little more build-up to 'A Lovely Night', particularly some broader hints beforehand that Sebastian was interested in Mia, and wasn't a complete jerk. However, it was still my favourite number. I think it 'did some work' in progressing the characters' relationship somewhat throughout the course of the number. The other numbers were nice, but IIRC they generally had the characters just baldly elaborating on things that they already felt, and knew that they felt. The song itself also mitigates its slight out-of-nowhere-ness to some extent by making that part of the joke - "We don't even care, we barely know each other, so why would we do a big song and dance - oops, here we go". It is a bit random, but sometimes initial attraction is indeed random and doesn't make rational sense, so whatever.
I think it's also a bit thrilling to see our leads sing and dance alone/together for the first time in that number. Not because they're the greatest triple threats ever, but because we're seeing that meeting one another is metaphorically making them sing and dance, even though they don't consciously realise it yet.
(Just thinking about it now, I realised it's a bit of an 'If I Loved You'-lite moment, complete with bench - and it seems that's what Pasek and Paul were going for - http://www.lamag.com/imagining-l-a/story-behind-music-la-la-land/.)
Incidentally, despite my defense of this number, I do agree with a lot of the criticisms mentioned in this thread. The movie is pretty to look at, the actors are likeable, the plot is meh. (Although, a few of the revered classic movie musicals' plots were pretty perfunctory as well.)