During the days of the German empire, what regions of the country would see themselves as Prussian, and which parts would see themselves as having been conquered by Prussia?

The question is ambiguous, as you don't say which "country"'s regions you mean. The regions of Prussia? Or the regions of Germany? Interestingly, there are parts of both that would have rejected the idea of Prussian-ness.

#Parts of Prussia that weren't really Prussian

So this is a bit of a personal one to me, as I am a Rhinelander, a region in Germany that was taken by Prussia after the Napoleonic Wars and that never really got into the Prussian feeling - for one particular reason: Catholicism.

You see, Prussia was very Protestant. The kingdom's very essence is founded on a crusader lord rejecting catholicism and becoming a feudal king of protestant kind instead.

Here is a confessional map of Germany around the year 1890. It shows deep protestantism in orange, deep catholicism in blue and the mixtures in the purple-red-ish colors (see the legend; the left column is catholics per 1000, the right column is protestants per 1000).

Not only can you see the survivors of Austrian-style catholicism in southern Silesia that was taken by Prussia during the Seven Years' War, not only can you see where Germans and Poles intermingle - most of the Germans near the Polish border were Protestant, whereas the Poles are almost exclusively Catholic across the board - you can also see the traditional Catholic strongholds in Protestant-leaning Germany. Those being the Rhineland and Westphalia in the west, French-influenced Alsace-Lorraine in the southwest and, of course, good old Bavaria.

Anti-Prussian sentiment in the Rhineland went so far that during the 1923 crisis in Germany there was an attempt at forming a French-aligned and Catholic Rhenish Republic in the Rhineland. The attempt ultimately failed, but had several interested supporters and observers, including the later West German chancellor and long-standing mayor of Cologne Konrad Adenauer.

#Non-Prussian German lands that didn't dig Prussia all that much

Now, in the world of realpolitik, both conquered North Germans like the Hannoverians (although they in particular still supported their own royal family over the Hohenzollerns) as well as South Germans that hadn't been included in the so-called "North German Federation" (read: 'Greater Prussia') in 1867 recognized that Prussia took the dominant historical and social position for a good reason: It was the largest, most populous and most active state of reunification, and hence, even hardcore Bavarians did not reject the Prussian King as the only viable candidate for German Emperor.

But speaking of Bavarians, the inclusion of Bavaria in the German Empire started a longstanding tradition of "Bavaria very grumpily telling Germany to get off its damn lawn". Bavaria was always the loudest voice for decentralized government and federalism - and Bavaria too in 1923 had a serious threat of secession from the Berlin government that was perceived as a Prussian monstrocity.