Sounds like a low end cyclocross bike with Sora shifters. These can take tires from 28 to 42 mm wide. so start with something in the middle like 35 mm. You can then decide whether you need to go fatter or thinner depending how much you slow down and unweight when you hop the curbs. Specialized Tricross, Kona Jake and Bikesdirect have models in this price range, but ask in your local bike shop. People talk down Sora shifters on these forums, but all Shimano shifters work well if adjusted right - Sora are not suitable for riding fast in a close pack of riders, but I think they would be fine for the sort of riding you describe. A touring bike would also take the fatter tires but I think they come at a higher price.