Let's give the OP a hand and say for the sake of argument some sort of treaty is signed, not a mutual defense pact or anything, but a precursor to Seward purchasing Alaska. Maybe a most-favored nation reciprocity between the two, special rights in Alaska. Russia had a previous attempt on Hawai'i perhaps Russia agrees to formally denounce any claims based on previous trading posts and recognize a US sphere of influence, maybe the US recognizes Russian border claims against British claims in the Alaskan panhandle in return. It doesn't have to be much, just the beginning of a good friendship.
Probably doesn't do much as far as butterflies- perhaps cooler US-British relations but not by much; perhaps the US and Britain have a harder time coming to a compromise on the Alaskan/British Columbia border (but the US got just about everything it wanted in OTL anyways); perhaps Teddy Roosevelt mediating the Russo-Japanese War is even more pro-Russian though I can't imagine that's possible, Teddy saved Russia's ass. Don't think it could have led to such good relations that Teddy drags us into a war against Japan and turn the tide for a Russian victory but maybe with another POD or two someone could make a realistic TL where Roosevelt brings us into war against Japan. Does this put Japan on the Central Powers side during WWI, or perhaps Japan is so isolated they don't join WWI against Germany or invade Manchuria and Japan doesn't join the Axis and the Pacific theater of WWII doesn't happen or if it does, Japan sees an America led by another Roosevelt and wants revenge for what happened 40 years earlier. Lots of possibilities.