Away just means away, i.e., away from home, but doesn't necessarily mean out of town. You might have been staying in town at a friend's house. But it sounds like you really were out of town, and thus you can use either one. They are both very commonly used phrases.
Of course, if you really don't want to give any details you can simply answer:
No, last week I wasn't at home.
As per comments, there's no real difference between the two idioms.
In other contexts (such as programming) an instance of something means an incarnation, actualisation, realisation (a real thing, as opposed to a definition of that thing). And an example can often mean an instructional case (perhaps specifically created for educational purposes).
But both for instance and for example are used in exactly the same way to introduce a specific illustrative case (or cases) - often with the implication it's just a random selection from many possible alternatives.
OP has already established that for example is more common (as my link shows, it's been increasingly displacing for instance over many decades). Initially, I was prepared to believe this might justify saying that for instance is "more formal".
But in fact I don't sense that myself, and I find no evidence for the idea. Consider these usage figures...
1a: for example I have (1,100,000 written instances in Google Books)
1b: for example I've 104,000
2a for instance I have 704,000
2b: for instance I've 76,500
In both cases the "informal" contracted versions account for about 1 in 10 usages, which strongly suggests no significant difference in terms of formal/informal register.
So my advice to OP is to accept for instance as an exact synonym whenever he comes across it, but to stick with majority/modern usage and always use for example in his own speech and writing.
Best Answer
No, it isn't.
The construction is
"If it were not for that coat, [then] I would not recognize you."
or, in the past tense:
"If it had not been for that coat, [then] I would not have recognized you." (Older version = "Had it not been for that coat, [then] I would not have recognized you.")
Both if clauses are in the subjunctive because he is in the coat and you did recognise him.
You cannot omit the bolded words. Words are omitted when there is a reasonable expectation of the listener being able to supply them.
It is possible to use "if not X then Y," but X and Y must be noun phrases:
A: "Take a coat. If not the green one, then the other." Note how the same omitted verb is provided (take) and is then omitted in the if clause.