Since you're rolling on two wheels, you need to be especially careful about slow leaks, nails, screws, glass, or anything else that might be stuck in one of your tires. Do a thorough visual check to be sure your tires look like they're in good condition, with no cuts or nicks or foreign materials lodged in them. Even sharp rocks can cause serious tire damage.

Spin the wheels around so you can see the tire from all angles. It may seem like a small thing, but you're trusting your life to your rubber. A sudden tire blowout on a car is inconvenient. A sudden tire blowout on a bike can result in serious injury or death, especially if it's your first time out and you haven't gotten used to riding yet. Take a couple minutes to check, and there shouldn't be any reason you can't have an awesome time getting to know your bike.