I love massive, completist geographical projects, and a bike is an excellent way to set one in motion. Get as big a map as you can and a marker and start shading in street as you ride them.
I went a little crazy in Santa Cruz with this in May of 2008 after a breakup and got a compass to mark off concentric circles from certain locations. I've now been on more than 99% of the paved roads (and some unpaved alleys) west of the river in Santa Cruz--probably been on every street except a few up off Empire Grade by campus. (Empire Grade ate a frame when I was rocking a single-speed; it's hard to crank up there.) It was a fun way to plan day trips and lunch breaks from work, and great for building an intuitive sense of how the city fit together in ways that were intensely personal. I've had situations where I'm leaving someone's house in a neighborhood I rarely go to but still have a mental map of the entirety of the surrounding streets. I grew my own heads-up display, basically.
It's not necessarily for everyone (I really, really like maps). The great part about grandiose plans is that you can ignore them and just get lost and have fun. I ended up cruising down a lot of residential streets and sketchy areas and boring subdivisions, (and got a few odd looks when I would bike by the same intersection three times in five minutes, or up a short dead-end street only to turn away grinning) and it got a lot harder to "knock off a few streets" as the streets I hadn't been on receded increasingly far away.
Restlessness is one possible side effect, too. Having been on every street on the West Side, it's impossible for me to get lost or make new street grid discoveries, and the challenge of getting to the new ones can seem insurmountable. The new environments to map are farther off, and this detracts from the spontaneity of the original experience. But that's the beauty of it all. I get to see much more of the city around me than the paths of home-work-bar-beach. All the tiny little nooks and funny ways to hack the city to meet my needs, the shortcuts that wouldn't occur to people--they really help keep my physical surroundings an organic whole.
(walking your town would be a better manifesto, but these are some notes from 2008 that I've decided to transcribe and get out of my hair. Plus I should be tuning my bicycle, and bicycle theory is a great way to procrastinate on that.)