Are there some popular journals in the field of theoretical CS that serve the kind of purpose that a journal like "Physics Today" does for the Physics community ?
From the information I could find online, I assume that the purpose of "Physics Today" is to summarize the incredibly vast field of physics and promote results that are considered important enough to be known from researchers with a different specialization from the subject matter. The focus is also on newly published results, rather than re-examining classical ones or establishing a "must-know" basis.
With this assumption, I believe the answer is no. The field has embraced Web technologies to a degree where results are usually known months before their official publishing in conferences and years before the journal version is out, with preprints being available typically via arxiv and rigorous discussions being held in popular blogs (for example Lipton&Regan, Fortnow&Gasarch , Aaronson ), TCS+ and questions appearing on this site as well.
Perhaps the one that comes the closest is Journal of the ACM (JACM).
See also this question.