James was bored. James was bored, and he wanted to fly, and maybe have a game of Quidditch. He wished he had slept with his Nimbus 1000 [or even his Silver Arrow, though it wasn't quite as good], so then he would have brought it as well as his wand. Still, he had his wand, and he had read Quidditch Through The Ages enough times to practically memorize it and the basic theory that went into broom making (okay, maybe nothing other than the fact that it had a cushioning charm on it, but he could figure out the rest), so he could
probably build a new one.
He knew though, that it would probably take more than just him and his extensive knowledge to build a broom. He knew (or thought he knew, at least) that Sirius liked Quidditch, and he remembered that the twins' brother, Charlie, though not yet Hogwarts age, showed great talent for the sport (or, at least for flying), and, though he didn't know Tonks (or so he thought), he
did know she at least had the same magic as him.
He tried to think of the other people in the park, and found that he couldn't, so, he began writing his letters.
( Letters to Fred, George, Tonks, and communication with Sirius )EDIT: After sending off his letters, he laid out in the sun to wait for noontime to come. And then a couple of other young wizards swam into his mind. He sat up and cursed, wondering how he had forgotten that Kira and Setsuna had been Hogwarts students as well.
He quickly scribbled them a couple of letters, and sent them off.
( Identical letters to Kira and Setsuna )