Well, first we must consider where Stitch has not yet been. We can assume that being a citizen of the world he would want to get a taste for its population before diving into things. He's already gotten a sampling of Hawaii, Japan, and Eastern China, and he has yet to see the sights of Europe, Australia, and South America. It would not be unreasonable for him to find his way to Brazil or Peru, Sydney or Perth, and the United Kingdom or France, among other candidates.
In any case, Stitch's harem would soon take root upon the completion of this first journey; he would then go across the world in his stolen police cruiser -- a red one, of course -- and use his knowledge of doggery and dog-related antics to woo young girls into accepting him, after which he then reveals himself as an alien and invites them to join him at his private villa off the coast of the Caribbean Islands, a flotilla placed within No Man's Land where the laws of civilization cannot touch him but the girls he's met can.
So I'd say it would take Stitch about another three years before he has his harem ready.