According to the Daily Mail online, Macca has designated "Here, There and Everywhere" and "Blackbird" his two favorite entries from The Beatles' catalogue. This sounds about right, I think: A pair of time-tested classics, one somewhat lesser-known among very casual Beatles fans ("Here") and the other an earnest crowd-pleaser ("Blackbird"). They're very Paul songs, gentle and full of sentiment. Who would've been surprised, though, had he decided on "Yesterday," "Penny Lane," "Hey Jude," "Let It Be," etc.? Unlike John, Paul isn't one to look back on The Beatles' output with contempt and scornfully rue what his youth wrought. Paul indeed seems to cherish most of his songs, regardless of the criticism that's been heaped on many of them over the years (particularly those from the post-Beatles era, of course).
Let me add that the choice of "Blackbird" or, rather, its seemingly hallowed status, has always puzzled me. I've never been able to connect with the song; it hasn't clicked for me. When I listen to "Blackbird," I hear something dull, ponderous, bereft of color, and not even terribly emotive. I realize that Paul's motivation for penning the song - as a response to racial upheaval in America - lends it a certain moral and historical appeal, but that only goes so far.
If I was Paul and had been asked the same question, I would've replied with "I've Just Seen a Face" and "Two of Us." I love both dearly.