It could have been a lot nastier but I think the satellite states in Eastern Europe are the wrong place to look - most of them really just wanted to transition and knew that raising border claims was a quick way to get put in the naughty category by the institutions they were looking to join.
Rather, Russia could have broken up even more - there was a movement for Tatarstan independence that was solved by essentially devolving a lot of sovereignty, for example. The North Caucasus had the Chechnya problem, but Dagestan also had separatist tendencies.
I would imagine if Gennady Zyuganov took over in 1996, you might have seen hostilities in Chechnya re-emerge earlier than in OTL as there was significant criticism of Yeltsin over the uneasy truce. A Kravchuk victory in 1994 in Ukraine might also tip off a regionalist conflict if cooler heads do not prevail - the Communist Party in Ukraine after all was of the Zyuganovite tendency and was significantly more radical in the 1990s than the Party of Regions would be in the 2000s.
The Georgian Civil War could have been much bloodier and long lasting had Shevernadze not taken over after the coup, as the Zviadist tendency was significantly less willing to bite its tongue and allow for the OTL status quo and Russia could have been drawn much deeper in.
One also must consider what would have happened had the National Salvation Front succeeded in 1993 - you might have had multiple revanchist conflicts emerge as public opinion was furious over the ramifications of the dissolution by then. What happened in OTL of course was terrible for Russian Democracy, but the alternative might not have been much better.