The home of Amaterasu Ōmikami and many other kami in Shinto myth is Takamagahara, or possibly Takamanohara. In Japanese, it is written with three characters, meaning “high” (“taka”), “heavens” (“ama”) and “plains” (“hara”). The last “a” of “taka” and the first “a” of “ama” merge, making “Takama”, and then “hara” goes on the end. I normally translate it as “the High Plains of Heaven”. However, there is no written character in the Japanese corresponding to “ga” or “no”.
“Ga” and “no” are both possessive particles. “Ga” is from old Japanese, and even by the eighth century, when we have the first written records of the language, it seems to have been old, used mainly with pronouns. It is still used in a few fixed phrases today: “wagako”, for example, means “my child”. “No” is the modern possessive particle, used with anything. “Watashi no ko”, for example, would be the standard modern Japanese way to say “my child”, although you would often use the fixed phrase instead.
The original pronunciation was “Takamagahara”, and that seems to be well established, suggesting that we have early texts that give the full reading. (I would expect this to be true, as the word appears in the Ōharaëkotoba, which was written out for recitation and analysed repeatedly over a period of more than a thousand years, but I do not personally know of any particular ancient source with the full reading in.) However, these days it is more common, but not universal, to refer to “Takamanohara”. Jinja Honchō, for example, always uses the “no” reading if they write it out in full, or if I need to write it in English for them.
“Maga” is the old Japanese for “evil, misfortune, pollution”. One of the kami born when Izanaki purifies himself on his return from Yomi-no-kuni is Ōmagatsuhi, where “maga” is written with a character that makes its negative meaning clear. The belief in kotodama, the power of words in themselves, means that some people do not like to say “maga”. Thus, they change the possessive particle so that the sound is “mano” instead.
As I mentioned earlier, both readings are in common use today, so it is not possible to say that one is “right”, or even “better”. However, if you don’t like the associations of “maga”, you should feel free to use “Takamanohara”.