If you start at NCAR (the big building on the hill at the end of Table Mesa Drive in South Boulder), there are lots of good trails that aren't too difficult. If you are feeling ambitious, you can hike to the top of Bear Peak (takes a few hours) from there. There is also a cool cave.

I love hiking up to the second flatiron. SOmetimes you just can just make your own trail. It can be kind of dangerous, but loads of fun.

I think the best hiking trails by far can be found by going up Canyon and exploring the trails of Boulder canyon. There are miles and miles of trails wound throughout the canyon, including hiking and other social trails. What's really great about the canyon is that its close and offers access to tons of trails (sugar loaf road, boulder falls, lefthand canyon, nederland etc.), and variety of terrain, all with the creek rushing by below you. The flatirons are super scenic as well, but much too touristy and popular for my liking. There is way too much other awesome stuff close to hike the flatirons more than a few times.

Chateautqua!

I think Chataqua is the best to start off with and it has a really great view for being so close and not as long as the full day hiking trails