I want to write "I will go to the convenience store with my friend tommorow" I wrote 「私は明日にコンビニで友達と行けます」. Is the grammar correct?
I think it’s wrong. I would write it like this: 「明日、友達とコンビニに行きます。」, which is hopefully correct. Also, I think that 行けます means “to be able to go”. I think you should use 行きます.
From what I know this is correct. I'd personally switch に for へ (used more for specific locations) though both options are fine. You could also say 行くつもり as in "I intend to go".
Just remember, if you add つもり, you need to end the sentence with です (or another variation of the copula). It is not grammatically correct to end with つもり, since it is a noun, even though it is often translated as if it is a verb
"(I) intend to go to x."
More literal translation:
"It is (my) intention to go to X"