I am going to GO sit in the back is correct, but it is better to say I am going to sit in the back I am going to buy something to eat is correct I am going to go buying something to eat is wrong

I am going to go buy something to eat. I'm going to get some pizza. Who wants some?

I am going to go sit at the back. -- This is correct I am going to go buy something to eat. -- This is correct I am going to go buying something to eat. -- This is arguably correct, but it's the most controversial of these sentences because it's so inefficiently worded (but not technically incorrect). I am going to go and buy something to eat. -- This is correct. I am going to go to buy something to eat? -- This is correct. Of course some of these sentences are more efficiently worded than others - lots of people here have expressed their preferences. I'm just saying where something is technically incorrect or not.

I am going to buy something to eat