It is hardly possible to tell, even briefly, about everyone. We have selected seven of the most likely options. Russian America is not included for the reason that it has already been a Russian colony for a long time.
Gilan and Mazandaran (Northern Iran)
In 1722, after the end of the war with Sweden, Peter I undertook a campaign against Persia. The troops marched both along the Volga and the Caspian Sea, and by land along the western coast of the Caspian. As a result of Russian victories in September 1723, a peace treaty was concluded, according to which Persia ceded to Russia not only the present Dagestan and Azerbaijan, but also the entire southern coast of the Caspian Sea - the present-day Iranian provinces of Gilan and Mazandaran.
After the death of Peter the Great, the new rulers of Russia considered it too burdensome to hold on to these distant lands. In 1732, during the reign of Tsarina Anna Ioannovna, an agreement was concluded in the city of Rasht (in Gilan), according to which Russia, without any compensation, renounced all the territories conquered by Peter from Persia.
It is interesting that in 1920 on the same lands, the Bolsheviks created the Persian Soviet Republic, which existed for one year.
Malta and the Ionian Islands
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In 1798, the Sovereign Council of the Order of Malta appealed to the Russian Emperor Paul I with a request for patronage and elected him as its Grand Master. The island of Malta itself was captured by the French at this time. In 1799, Paul I began a war with France, during which Russian troops, supported by the fleet, captured the Ionian Islands. In 1800, Paul made peace with Bonaparte.
The new situation made it possible to exchange the Ionian Islands for Malta from France. After England captured Malta, Russia could settle in the Ionian Islands. Formally, a republic was established there under the joint protectorate of Russia and Turkey. But Paul's son Alexander I fell out with Turkey in 1806, and in 1807, according to the Peace of Tilsit, ceded all rights to the Ionian Islands to France.
Hawaiian Islands
The Hawaiian Islands, first seen by Spanish sailors in the 16th century, were not visited for a long time by Europeans. At the end of the 18th century, they were first studied in detail by the English navigator James Cook. Thereafter, Europeans, especially the British and French, began to show interest in the archipelago. But there already existed its own statehood, created by the aborigines - the Kanaks. In 1810, the local chieftain Kamehamea united all the islands under his rule. And in 1815, the Russian American Company (RAC) tried to settle there and annex Hawaii to Russian America.
In 1816, RAC Captain Georg Schaeffer founded three Russian forts in Hawaii. However, the following year, the RAC was driven out of there by an American pirate expedition with the help of the natives. The RAC project on an armed expedition and the colonization of the Hawaiian Islands was presented to Alexander I, but the king rejected it.
In the Pacific Ocean, Russian expeditions of the early 19th century discovered a number of islands that could belong to Russia by right of discoverer: the Kruzenshtern reef and Lisyansky island in the same Hawaii, the Russians islands in the Tuamotu archipelago, Senyavin islands (in Micronesia), etc.
New Guinea
In the 1870s-80s. Russian traveler and ethnographer N. N. Miklouho-Maclay explored in detail a part of the northern coast of the island of New Guinea. He repeatedly tried to interest the government and the Russian public in the colonization of this territory. But his first draft, presented in 1875, came across a government refusal "due to the absence of Russian interests there."
But the governments of England and Germany did not at all consider that their interests were absent there. In view of the beginning of the colonial expansion of the Europeans, Miklouho-Maclay again and again turned to the government and to the Emperor Alexander III himself. In 1884, a special government meeting rejected Maclay's project on the pretext that Germany had already claimed rights to this territory. Maclay addressed the public through newspapers and collected 1200 signatures of those wishing to participate in the creation of the Russian colony. But in 1886 Alexander III forbade any further progress in this matter.
Abyssinia (Ethiopia)
At the end of the 19th century, European powers became interested in Ethiopia. In 1889, the Russian traveler N. I. Ashinov gathered 150 Cossack volunteers and founded a colony in Djibouti. But this territory was claimed by France. Ashinov's colony was destroyed, the surviving colonists were taken to Russia, where, in turn, they were repressed by the tsarist court.
In 1894, Italy tried to take over all of Abyssinia. Russian traveler N. S. Leontiev was at this time in the diplomatic service with the negus Menelik II. He managed to persuade Russian society and the government to help Ethiopia. Negus defeated the Italians in 1896 and expressed his readiness to go under the official protectorate of Russia. But Nicholas II did not want to accept Christian Ethiopia under his protection, fearing complications in relations with European countries.
Manchuria and Korea
In the last years of the 19th century, Russia began to penetrate into Northeast China and build the Chinese-Eastern Railway and the Port Arthur base there. The city of Harbin, the largest Russian colony in China, was founded in Manchuria. On some Russian maps of that time, Manchuria was depicted as part of Russia, acquired during the reign of Nicholas II.
At the same time, Russian companies received concessions in Korea, and the Russian envoy in Seoul enjoyed tremendous influence over the royal court of Korea. This activity of Russia provoked opposition from Japan. Everything was decided by the Russian-Japanese war of 1904-05. Having suffered defeat in it, Russia was forced to abandon influence in Korea, and its presence in Manchuria was limited only to the northern part.
Bosphorus, Dardanelles and Great Armenia
During the First World War, in 1916, the Foreign Ministers of England, France and Russia signed a secret agreement to partition the Ottoman Empire. After the war, Constantinople, the Bosphorus and Dardanelles straits with adjacent territories on the European and Asian shores, as well as the territories of Eastern Anatolia inhabited by Armenians before the war with access to the Mediterranean Sea (Great Armenia) were to withdraw to Russia. The agreement remained unfulfilled due to the fact that in 1917 Russia, in which the revolution took place, withdrew from the war.
Probably, if the annexation of Constantinople was carried out, then it would have become one more, along with Petersburg and Moscow (and possibly the first among them), the official capital of the Russian Empire.