The best replacement for time magazine is newsweek.

The best alternatives to time magazine are rated as following:
★★★★★  newsweek
★★  economist
★★  newsweek magazine
★  national geographic
★  new yorker
★  newsweek economist
  time magazine
  week
  time

Your alternative for time magazine is not listed? Suggest!
Speaking about time magazine, one probably shouldn't forget about free watch.

Other search terms related to time magazine and their ratings are:
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Google Trends

Scale is based on the average worldwide traffic of time magazine in all years. Click on graph for more.
time magazine
newsweek
economist