You are new to the area, so you have a lot to choose from. Heinen comes to mind quickly. Danskin Peak is incredibly cool and would be a hike from the south (not using the road). Kepros would be cool if you haven't done it. Those are within an hour drive (or so).
Heinen:
http://www.idahosummits.com/Heinen/heinen.htm
Danskin:
http://www.idahosummits.com/danskin/danskin.htm
Kepros:
http://www.idahosummits.com/kepros/kepros.htm
Rough Mountain is often forgotten and not near Idaho City, but it is cool. It is in the Owyhees and is snow free now. I had fun when I did it. That is another possibility
http://www.idahosummits.com/win_spr_2003/win_spr_2003.htm#rough
I could go on and on if you'd like
