There are actually interesting, fast moving things to be seen in the sky all the time. It’s just that most people aren’t looking up enough to notice them. A lot of satellites make obvious tracks across the sky, as long as you know when and where to look. Few things are as bright or obvious as the International Space Station or an orbiting space shuttle, but there are still a lot of others. Iridium flares (the brief but VERY bright glinting of sunlight off a particular type of communication satellite) are some of my favorite things to catch.
The Heavens Above site is a great place to see what kinds of satellite passes are going to be visible for your location in the near future. Just tell it your location (otherwise, it defaults to the intersection of the prime meridian and equator, which isn’t anywhere good), and you get a list of all the coming attractions in your particular night sky. The only real catch is that locations for satellite tracks and flares are given as altitude/azimuth angles. That’s not complicated at all, but it does require that you know where north is from your backyard, and that can get reasonably close to guessing how high up, say, 57 degrees is. And actually, for some things, Heavens above lets you clock on a start chart to see the path of the object. It does that for the ISS…I just wish it did it for Iridium flares. If I want to be double sure I don’t miss a bright Iridium flare, I look up that Alt/Az coordinate on a star chart and figure out what bright stars or recognizable constellations are nearby, so I don’t get lost.
In any case, you should be able to catch the ISS for a few days in a row every month or so. The only trick is knowing when to look, and Heavens Above is great for helping with that.