Some alleycats require racers to ride fixed-gear bikes, but most are open to anything with two wheels and a chain, from mountain bikes to clunky commuters. Beyond the bike, here are a few key items not to be left behind.
Map: Bring a detailed map of the city, or use a map program on your phone. Checkpoint stops are often at esoteric addresses and out of the way places. Even if you think you know the city you're going to need some help on the navigation front to complete a course.
Marker or Pen: Bring a couple. You'll need to write down clues, draw routes on a map, et cetera.
Cash: Entry fees are often nominal (or free), but carry some extra scratch in case you need to jump on a train or bus somewhere on the course.
Map Bag: Basically a flat Ziploc-like bag used by orienteer to protect their charts. I use one to prevent my paper maps and manifests from being ruined by sweat.
Water: Don't think you can skimp on hydration just because you're in a city. I bring two full bottles or, for longer events, a bladder in a backpack. Some alleycats can last two hours or more, and you're often sprinting and stopping fast, or cranking hard the whole time.
Food: Some alleycats stretch 50 miles through a town, so you need calories and carbs to power through to the end. I bring gels and energy chews on longer events.