Learn English – Is ‘Not a peep’ an idiom, or just plain statement

I don't think it is an idiom, but it is used routinely enough to be understandable. As you surmised, to think past something means to think beyond something, to jump to the next thing, instead of spending time on the "something" currently in front of you.

Also, to think past yourself means to think of things other than yourself. For example, in this Utah State Today article:

Noted humanitarian, award-winning and best-selling author, documentary photographer and Navy SEAL Eric Greitens told Utah State University graduates Saturday that they will be at their strongest in life’s journeys when they are serving others. While speaking to Utah State University’s graduating class of 2012, Greitens told the students to think past themselves and to serve something larger.

As you figured out, in your example, the traveler was ready to dismiss Lisbon because she wanted to be gone from there and travel on to what she thought was the much-more-interesting destination of Oporto. So she wasn't giving Lisbon any thought at all, but was instead already anticipating Oporto. By looking ahead to what was coming next, she was missing out on what was right in front of her.

Normally, not to x or anything is followed by a but, like this:

Not to generalise, but women often spend too much on shoes they never wear.

Here, it is short for [I do/did] not [mean] to generalise, but... It is a caveat, and a warning that what you are about to do (or have just done) may be interpreted in a bad way.

In casual speech, or anything is often tacked on to make the generalisation seem less explicit, less important, as in: "I may be generalising here, or I may be doing something else—it doesn't matter anyway—, but...".

Using not to x or anything without a following but looks like sloppy writing to me for a serious article, which is probably part of the reason why it confused you: the generalising statement ought to follow, explaining the caveat—but no such statement follows here, at least not immediately. It is not a grave sin, but it's not exactly eloquent here. Most writers would only use that in a very casual context.

Based on the rest of the article, I believe the generalisation is supposed to be the writer's theory that "[m]ore recently, however, Romney’s luck has turned", as mentioned at the start of the paragraph. The statement by Romney about the 47 % is supposed to be an example supporting the theory. But at the same time it is probably a sarcastic quip referring to Romney's own generalisations in these quotations.

The this that comes immediately after is unrelated to the not to generalise: it refers to the 47 % statement, the example supporting the theory. It is short for something like this [was/happened], or [and notice how] this [was]. It is meant to make clear that there is a connection between the previous example and what follows, Romney's statement about Obama.