I'm a new transplant too. I moved up from Missouri last August.
There are so many trails it's hard to pick. I highly suggest you either get a few books for the area or get a http://www.trails.com account to find lots of trail listings. I'm a bit north of you (Longmont) and really enjoy the Indian Peaks Wilderness area but you've got thousands of great trails between me and you.
If you end up staying in Colorado Springs you'll want to start training to start bagging 13'ers and 14'ers. Lots of obtainable peak bagging in your area even for the steady day walks. Of course if you want to come up and nail Long's Peak give me a shout, it finally looks like it's melted off for the summer and I need an excuse to tackle it.
If you end up in Denver you'll be around the Roosevelt national forest as well as some others south of Denver, but everything in Denver is a bit of a drive to get away from the crowd.