The old soviet bloc nations wanted to join NATO for several reasons.
First, joining NATO is seen as a stepping stone to join the European Union. Obviously any leader of any Eastern European nation wants to join the EU to give their citizens the right to travel and work in the West, and allow western companies to set up factories and businesses in their country to take advantage of low wages and tax incentives.
Not to be too obvious, but any CEE country that is allied with Russia either economically or militarily will not have a hope in HELL of joining the EU.
For its part, Russia also does not want to have close strategic relations with a country that is in the EU.
Countries that want to join the EU need to beware of joining Russia's Eurasian Economic Union (EEU).
The NATO-EU-EEU conundrum was played out in Ukraine.
The fact is, nations in CEE want to join the EU, and they see joining NATO as a first step. Montenegro is a good example: they applied to EU and NATO as soon as they became independent. They are now part of NATO, and are hoping to become part of the EU soon. Croatia is another example. Do you think they were really afraid of Russia attacking them? Or did they want to join the EU. In any case, they managed to become a NATO member in 2009 and then achieved EU membership in 2013.
But the best example are the Baltic States. As a reward for their joining NATO - and happening to be located right on Russia's borders - they were given SIMULTANEOUS membership in both NATO and the EU.
Estonia, Latvia and Lithuania all became member of the EU as well as NATO in 2004.
That was unprecedented, and very unusual, but I guess George W. Bush really wanted to "lay down a marker" and poke Russia and show Putin who's boss by putting three new NATO members on Russia's border "overnight".