I'll agree with CaptainColeslaw's recommendations. For a long time, Igel Argern was a cult hit on the site. It's very much a strategy/luck mix. 10 Days is always fun too.
Cosmic Wimpout is might a bit much on the luck side for you.
Axis and Allies is the most popular, and probably the most directly Risk-like...but not what I would call newcomer friendly. There's a lot of rules in it.