Welcome to the InDesign Forum.
ID is a page layout program, and well suited to magazine production. You might find some templates by googling InDesign Magazine Template.
Illustrator, which you asked about, is a program for creating vector art, and is probably not well suited to creation of an entire magazine.
There are some free InDesign Templates here: https://indesignsecrets.com/resources/indesign-templates
If you're a beginner to InDesign it would be worth taking some lessons as it has a steep learning curve.
TrainSimple.com and Lynda.com have excellent online tutorials and there's also a very good "Quick Start" book: http://www.amazon.com/InDesign-CC-Visual-QuickStart-release-ebook/dp/B00ND5YY1U/ref=sr_1_s c_1?ie=UTF8&qid=1449162002&sr=…
Just so you know, a magazine would normally be made with three apps:
Illustrator - for drawn pictures, diagrams, logos etc.
Photoshop - for photos
InDesign - to lay out finished pages (text here, pictures there).
If you try to find ONE app to replace Word you'll be disappointed.