The borders of the individual republics, while largely based on ethnicity, were far from democratically chosen.
With Crimea becoming an irrdentist topic in the last decade and large amounts of ethnic Russians throughout the new countries I'm shocked some type of war didn't occur.
I think it depends on what one means by peaceful.
While the collapse of the USSR was generally seen as peaceful by Western observers (usually because it was assumed that only a nuclear world war could end the country's existence), the collapse and disintegration of central Soviet authority spawned numerous small conflicts.
A short list through 1998 includes:
The Transdnistrian War in Moldova (1991-1993)
The Gagauz conflict in Moldova (1991-1993),
The Abkhaz-Georgian War (1992-1994)
The South Ossetian-Georgian War (1992-1994)
A civil war in Georgia proper in 1992
The Nagorno-Karabakh War of 1988-1994
The Tajikistan Civil War (1992-1997)
Russia itself went through the First Chechen War in 1994-1996, and the 1993 Constitutional Crisis that effectively resolved itself through a short civil war localized to Moscow.
A most of these conflicts have still not resolved and are regarded as "frozen conflicts ", which Russia has had varying levels of influence over.
As far as borders were concerned, beyond these conflicts there were border skirmishes in Central Asia, mostly between Uzbekistan, Tajikistan and Kyrgyzstan, especially over their extremely complicated Soviet era borders in the Ferghana Valley.
Belarus, Ukraine, Russia and Kazakhstan had less border issues, mostly because they were preoccupied with massive domestic upheavals and were more concerned with how to divide up the Soviet nuclear and conventional military arsenals than with the borders.