Learn English – Should I say “go out” or “go outside”

outside of is perfectly fine in this case. It may be of a slightly lower register than alternatives like "other than" but it is often used in the same register as expressions like north of meaning more than.

outside of : except for something; besides something. Outside of the cost of my laundry, I have practically no expenses. Outside of some new shoes, I don't need any new clothing.

I think my preferred translation in this case would be: other than

Sometimes, instead of "outside of classes," you might see:

outside the classroom

For example:

Most of what people learn in life was learned outside the classroom. Just because something was learned in a classroom doesn't make it more legitimate than other types of learning. (Reilly, 2009)

It is clear that a great deal of what is learned using computers is learned outside the classroom; at home, in vocational training settings, and at work. (Light & Littleton, 2002)

The CLEP involves a series of examinations providing college credit for life experience and knowledge gained outside the classroom. Hence, the program tends to be of benefit to older students who have been out in the work force for a few years. (Margolin, 1990)