Teddy Roosevelt mediated the Treaty of Portsmouth, that ended the war between Russia and Japan. TR watched Sergi Witte negotiate a treaty that was remarkably beneficial to Russia. They got off with light losses, despite being soundly beaten in the war. Witte took a lot of heat from Tsar Nicholas II's court. They even blamed him for the riots in 1905. Nicholas continued to hold a grudge against the US.
When World War One started, the United States lent money to Russia, sold them munitions and in 1915 took an order for some 1500 steam locomotives. The Tsar abdicated before the United States declared war on Germany, but in 1917 the United States developed close ties with the Provisional Government. They lent a lot more money and allowed Alco and Baldwin locomotive companies to sign contracts for another 3000 locomotives. The provisional government collapsed before many of the locomotives could be delivered. Some were cancelled and the ones that were embargoed were sold off to railroads in the United States. The large amount of money that the Provisional and Tsarist governments borrowed was repudiated by the Soviet Union and that was a major bone of contention between the USA and the Soviet Union.
Sources "The Historical Guide to North American Steam Locomotives" by George Druery
"The Rise and Fall of Great Powers" by Paul Kennedy

Culturally, the Russian relationship with the US was mixed with fascination and ambivalence. On one hand, Russian elites looked towards Western Europe for culture and tended to look down upon American pretenses. Even today, one of the highest praises to give someone in Russian is kulturnost (cultured in bearing and education). However, prior to WWI, there was a growing awareness and appeal of American modernity among both the Russian educated classes and the populace at large. Part of this was due to greater literacy and the Russian diaspora from immigration made Russians more aware of the US. In many respects, America was a model that Russians sought to emulate: a large country that had developed into the acme of modernity. One Saint Petersburg newspaper devoted a lengthy column to how Americans had made themselves happy and prosperous. Some popular Russian novels began to feature American characters and settings. For example, Pinkertonovshchina were a genre of crime novels that featured an American Pinkerton detective solving cases in the US tangentially involving Russian nationals. Such fascination continued even into the Soviet period. Even though the Bolsheviks could never accept American capitalism, they were always impressed (and envious of) by US skyscrapers and technological innovations for consumers. For example, Mikoyan on a visit to the US was deeply impressed by US hamburgers- which was an efficient proletarian snack.

sources

Gronow, Jukka. Caviar with Champagne: Common Luxury and the Ideals of the Good Life in Stalin's Russia. Oxford: Berg, 2003.

McReynolds, Louise. Murder Most Russian True Crime and Punishment in Late Imperial Russia. Ithaca: Cornell University Press, 2013.

Schlögel, Karl, and Rodney Livingstone. Moscow, 1937. Cambridge, UK: Polity, 2012.

Steinberg, Mark D. Petersburg Fin De Siècle. New Haven: Yale University Press, 2011.