Say the Russians win the Crimean War by exhausting France and Britain, and some 'status quo per ante' is signed.
The immediate cause of the war - France being confirmed as defender of the Holy Sites in Palestine - would be reversed,with Russia resuming that role. With the only powers in the region willing to stop it defeated, Russia probably will increase agitation among the Orthodox population to increase its influence in the Balkans and in Armenia. I don't think Austria will appreciate this, but since they have little chance against Russia themselves they might join in with annexation of Bosnia while balancing with Britain and France.
Domestically in Russia, impetus for serfdom liberation would probably be reduced, as army reform, political reform etc. Probably would lead to Russia being even more backward than reality, with much-needed reform probably happening after the next defeat at the hands of Britain and France (maybe like 1870s in my opinion). But Russian backwardness does mean that anarchism and communism might take a bit longer to take root, thus 'missing' the chances they got in OTL to be a serious force.
The damage to French prestige would be huge, and probably reignite agitation against Napoleon III's government. Could be beneficial for France in the long-run as it means Napoleon III engages in fewer adventures, though it does mean French help in Italy does not happen and so no Italy. For Britain, you'd probably see some panic regarding India in Whitehall and thus it might pursue a more belligerent role in the Middle East, esp. Persia and Afghanistan.
For Turkey, it's probably safe to say that Russia would attempt to re-establish the Treaty of Hunkar Iskelesi (1833), which would conclude an 'alliance' between Turkey and Russia while also giving Russia the right to intervene in the Ottoman Empire for reasons of 'security'. Also likely that the Tsar would demand that Turkey close the Dardanelles at Russia's request, or perhaps an even more favorable version where Turkey allows Russian ships free passage into the Med.