For instance, the Statue of Liberty came to the US from France and Canada getting tulips from Holland. I don't mean diplomatic gifts, such as cigars or booze or whatever that two leaders might exchange at a summit. I'm talking about monuments or the like that are huge and often enjoyed by the public.
in communist countries it was common. they called it "Soviet gift for xxx (Polish, Czechoslovakian, etc) nation".
here, in Poland, most known is Palace of Culture and Science.
but like always in communist coutries it trully not a gift, it have deeper meaning (like "we care about other communist coutries", or "we are better", etc), in broad perspective they were still in plus (Soviet Union imported from satelite countries many goods with very low prices) and in almost they wanted to increase popularity of communism in those coutries.
it's example from top of my head, there is more "gifts" from soviets to satelite countries, but i don't know that is the answer you want.
I don't know if it qualifies as lesser-known, but the flowering cherry trees of Washington, DC represent a century-long and ongoing gift exchange between Japan and the USA.
The idea of planting flowering Japanese cherries originated with one American woman's personal campaign, but when the idea finally took root, in 1908-1912 the Japanese government took the lead and donated thousands of trees from classic stocks in Japan. Since that time there have been further gifts, and cuttings from the Washington trees have gone back in return to Japan to help replenish and replace trees lost in Japan.
The National Park Service has a brief history here: http://www.nps.gov/cherry/cherry-blossom-history.htm
The Trafalgar Square Christmas tree is a Christmas tree donated to the people of Britain by the city of Oslo each year since 1947. The tree is prominently displayed in Trafalgar Square from the beginning of December until 6 January.