Compared to Germany's relationship with France, Poland, Benelux etc after World War 2, it's relationship with Russian has been at least decent, even during the Cold War and there seems to be remarkably little ill-will considering the atrocities committed by both nations during World War 2.
I would not really classify the Cold War relationship of the USSR and Germany (both the FRG and the GDR) as particularly good or amicable. During the period of 1948- ca. 1970, the relationship between the Soviets and the FRG was quite frosty. The CDU government of Adenauer and his successors was fervently anticommunist and frequently brought up the issue of German POWs languishing in Soviet captivity. The FRG government also staked a peculiar position that it was the sole legitimate German government and sanctifying all territorial adjustments of German territory in the war would have to be approved by what it construed as the true German legitimate government. The FRG's Hallstein Doctrine sought to erect a diplomatic cordon around the GDR and made it clear that it would consider it an unfriendly act if any nation extended diplomatic recognition to the GDR.
For its part, the Soviet Union often took a rather hostile line towards the FRG. One of the staples of Soviet and GDR media was that the FRG's government consisted of unrepentant National Socialists and other fellow travelers of fascism- for example, see this Soviet cartoon depicting a Nazi soldier running through Americas loose denazification and becoming one of the bedrocks of the FRG on the basis of his anticommunism. The idea of a covert fascist in the FRG became a stock trope in Soviet fiction and examples like Adenauer's Press Secretary Hans Globke, who was quite active in the Third Reich's government, added credence to this depiction of the FRG elite. The Soviets seldom balked at bringing up the past, especially if it could be used to publically embarrass both the FRG and its US ally, such as in 1961 when the Soviets appealed to the UN to extradite a Bundeswehr general, Adolf Heusinger, who had assumed chairmanship of the NATO Military Committee in Washington, DC. Heusinger was a former OKH chief of staff under the Third Reich and the Soviets alleged he was guilty of war crimes in that capacity. Although the FRG and the USSR had reestablished diplomatic relations in 1955, the FRG's position on the (non)status of the GDR added a great deal of tension as the Soviet position was that the GDR was a viable and independent state.
Even though the GDR was a satellite state of the USSR and the SED dictatorship was dependent upon Soviet support, there was relatively little trust between the Soviets and the GDR population. One common joke in the GDR reflected this fraught relationship: a teacher asked his student if the Soviets were either socialist brothers or friends, to which the student replied, brothers, because you can choose your friends. This discontent with Soviet forces and their close relationship with the SED boiled over in June 1953 with large mass protests in the country that had to be suppressed by armed force. Nor was the relationship between the Soviets and the SED particularly warm. Moscow tended to look askance at its SED allies' inability to put their own house in order and for their part, the SED leadership was sometimes afraid that the Soviets would sell them out to gain a reunified and neutral Germany. The SED leadership often maneuvered behind the scenes to get the Soviets to do their dirty work, most famously in the construction of the Berlin Wall, which many in Moscow recognized as a propaganda blunder but built in part because to stem the brain drain from the GDR.
Soviet-German relations only entered into a real thaw with the advent of the Ostpolitik of Willy Brandt which led to a normalization of relations between the FRG and USSR and the abandonment of the Hallstein Doctrine. Ostpolitik also established the idea that the GDR and the FRG had a special relationship and both would respect each other's uniqueness and independence, which would be one of the dominant leitmotifs for FRG-GDR relations for the remainder of the Cold War. One of the reasons behind this shift was economic. As the Brezhnev state sought to make up for shortfalls in its planned economy with the sale of oil and natural gas, the economic success of the FRG made it one of the major markets for Soviet fossil fuels. The FRG also became one of the major creditors for the GDR in this period. However, there was also political component to this as the Soviet leadership recognized that a constructive relationship with the FRG was more beneficial to Soviet interests than a hostile one. Here too did economic interests also emerge, as the FRG's leadership in the European economy made it a major player in European politics.
This economic strength of the FRG gave the Kohl government a degree of confidence and leverage to channel unification into terms favored by the FRG. Although memories of wartime atrocities can run quite deep- see for example Greece's very recent invocation of occupation reparations in the EU bailout- dredging up memories of the past can be quite counterproductive for inter-state relations, especially for a state as strong as the unified Germany.