Why? 'cause the Oregon boulevard was a little far from where he was, and he wasn't even sure if he can locate it on his own. It doesn't seem like a cab or public transport would pass by soon, it was still early, they don't move about by this time. Leonard does leave early for work, but not as early as this.
He knew why he wanted to get to the Oregon boulevard on time, he doesn't know Stella's schedule, he doesn't know when she'll leave her house. So it was even better to reach there and wait, than to reach there and she wasn't at home anymore. But as things were going like this, seems like his plan would spoil, not even a single cab has drove past. But he wouldn't give up just like that, this was something he planned, he wouldn't let it fail just like that.
