I think Signal's a solid choice if your friend likes thrillers. I would also recommend Two Weeks, which has very minimal romance and a fast-paced plot. Wanted is another thriller drama with no romance, although I personally enjoyed this one less than Signal/Two Weeks. Special Affairs Team TEN is another option if your friend is a fan of American crime thriller/procedural shows.
Cruel City and City Hunter are also thrilling and engaging, although both of these do include some romance.
There is no romance in School 2013 or White Christmas, so if you are looking for a school drama, either of these might work.
My top pick is definitely Two Weeks. It has more of that addicting "k-drama" feel to it than Signal has, so I think it'd be a good first drama :)