two things:
First, regardless of what they want, we've ALWAYS been pushing. You can look at the WIkileaks cables and see that... there's hard evidence of it.
And I've read (though I haven't personally seen hard evidence) that in the waning days of the USSR, our State Department repeatedly assured the Soviets we wouldn't expand NATO, and they gave their consent to German Reunification, and EU expansion based on those assurances, which we've repeatedly violated. Which is why I'd question anyone saying Putin is the one who needs to be stopped. The Russians certainly don't see things our way, and you have to imagine impartial observers who can read a map wouldn't either.
Second, as far as Eastern Europe wanting to be less under Russia's influence, that's probably true, although it doesn't necessarily mean they want to be under American influence.
And as far as choosing between Russian or American influence if they had to be under somebody's thumb, who knows? I suspect the younger folks in Eastern Europe might choose America, (although like a lot of things American, our myths of superiority are running on fumes at this point). This isn't the 90's or even the 00's anymore...
Older folks, who have to pay the gas bill to avoid actually freezing to death in the winter, and buy medications to stay alive do not see American influence as a fun Instagram alternative, but as a matter of life or death... Russia supplied cheap gas and cheap medication.
I saw those changes first hand last time I visited (albeit now 4 years ago). In the rural areas, or people on fixed incomes were burning trash to supplement the heat in the winter, and any money I sent was horded to afford next month's insulin or whatever.