In 1903, British Colonial Secretary Joseph Chamberlain offered 5000 square miles of British East Africa in an area that's now Kenya. The proposal was brought to the World Zionist Congress in Basel and received a decent amount of support - so much so that the Congress sent emissaries to the colony to investigate its potential usefulness as a new Jewish homeland. In the end, the proposal was declined at the next Congress in 1905.
Those who had supported the 'Uganda Scheme' actually split from the WZO and founded their own 'Jewish Territorialist Organization.' The Terrirtorialists sought to create a Jewish state anywhere and were happy to settle in East Africa rather than Palestine.
In addition to the Uganda plan, the Nazis themselves proposed a plan to settle Jews in Madagascar. Their goal was to transfrom Madagascar into a SS-ruled police state populated by millions of exiled European Jews. The plan had no interest nor cooperation from any Zionist organization.
Another plan constructed with little actual input from Jews themselves was the Soviet effort to create a 'Jewish Autonomous Oblast.' Stalin prompted its creation in 1934 as part of a policy to encourage Yiddish culturalism and thus avoid Zionism, which he saw as a threat to Jewish loyalty to the USSR. At its height, there were 30,000 Jews living there (mind you, entirely non-religious) - today there are maybe 2000.
One final plan worth mention is the Slattery Report, an US official commission that attempted to settle European Jews in four locales within Alaska. The proposal failed and also failed to garner any Jewish support. (Although it does provide the background for Michael Chabon's counterfactual historical novel The Yiddish Policeman's Union)
All in all, the only distraction from Palestine that Zionists ever seriously entertained was Uganda/Kenya. This plan got further than the others in that the WZO actually went and visited the land and there was actually a significant debate in the Zionist community about its feasibility - a debate that actually led to a split within the Zionist movement.
In addition to /u/amir-amozegh's post, I'd like to elaborate a tiny bit. The Nairobi offer came only after the British had attempted to negotiate with the Ottomans on a possible state in the El-Arish area, or the Sinai. However, the Ottomans had rejected these plans.
Source: Theodore Herzl: A Reevaluation Jacques Kornberg The Journal of Modern History, Vol. 52, No. 2 (Jun., 1980), pp. 226-252
It was not a jewish state, but I have read that there was also a proposal to create a settlement for ~50,000 Jewish people in the Kimberley region of Australia, in the 1930s, a quite remote area.
It was eventually vetoed by the Prime Minister, according to the source below, because of concerns that the people would drift from the settlement to the cities.
During the 1930s, Stalin established the Autonomous Jewish Oblast in the eastern USSR in an effort to attract Jews to the country and to Communism. Stalin reasoned that the Jews would be a likely ally of the proletariat due to a common history of oppression at the hands of bourgeois national governments. However, not many Jews immigrated to the USSR to settle in the newly-created autonomous oblast, especially as WWII began. After the war, Stalin's view that the Jews would most likely support Communism (as well as his hopes that Israel would join the growing Soviet sphere of influence) led him to be one of the first world leaders to recognize Israeli sovereignty. After the establishment of Israel, many Soviet Jews emigrated over the years with an even larger number leaving in the tumultous 1990s after the collapse of the USSR. The Autonomous Jewish Oblast still exists today, but with a greatly reduced Jewish population.
Edit: Just saw that /u/amir-amozegh mentioned the Autonomous Jewish Oblast in his post.
In 1939, Harold Ickes (US Secretary of the Interior) under Roosevelt proposed to move to Jews to Sitka, Alaska in what is known as the Slattery Report.
However, Roosevelt himself didn't support the plan and it was (obviously) never executed.
Sidenote; the Yiddish Policemen Union is an excellent book by Michael Chabon which takes place in this fictional Jewish settlement of Sitka, Alaska.