The joy of reading Descartes is indeed the process, the lyrical unfolding of a solitary mind trying to understand itself and the world. If you enjoy angsty first-person narrators (Sartre, Dostoevsky, Beckett), then you really must do read Descartes. Not that he was the first to invent the practice - there are plenty of contemplative mind at work bits in Augustine's Confessions, for instance - but he does it so beautifully, and it really does set the stage for the later versions.
One of the astonishing things about the narrative is how tangible it is. He's trying to figure out whether the universe exists, and meanwhile, you have these scenes where he's looking at a piece of wax, and it's so shockingly vivid, it's gorgeous. A nice example, incidentally, of the power of literature and its ability to evoke, and how it can be in a tension with the ostensible claims being made.
The argument itself is interesting, though flawed at moments. Though I probably should be giving some kind of analysis of its points, I won't, partly because I'm not really prepared to make one yet, and partly because I'd rather tell you, dear readers, about the beauty of the book instead. There are many arguments out there to read this work, but pleasure is generally not among them, and it turns out to be the best one of all.