You've got a good eye. Of course, there are a ton of books you can read (and websites, etc) that can help you learn more about both composition, and the technical side. (Understanding the technical is critical in being able to get the most interesting shots... auto modes tend to all gravitate towards a very basic look).
You should think about what type of shots do you want to take, do you want to specialize. Look up a couple of posts, you will see Zackiedawg does a ton of wildlife and birding. Look at Disney blogger Tom Bricker, who mostly shoots wide landscapes. I'm a bit of a jack of all trades, but some of my best shots are street photography -- just people out and about in the street, doing their normal thing. So finding interesting things to shoot, partially depends on what you want to shoot.
I strongly believe that for good photographs, LIGHT can be even more important than subject. Go to a park, or someplace scenic around where you live, either right around sunrise or sunset. See how the sky changes from about 30 minutes before and 30 minutes after. See how the light affects the landscape. And even if you aren't shooting the landscape, that light makes all the shots more interesting -- so even if you just want to shoot things around the park in that early morning or late evening light.
Interesting light makes every scene better:
Sunset over Chappaqua by Adam Brown, on Flickr
GrandCentral-55.jpg by Adam Brown, on Flickr
fallsunrise-70.jpg by Adam Brown, on Flickr
Cassady
