My name is Sasha and I'm dying to speak in English haha:)

I live in a small town and have been studying hard to learn English at my University.

Привет Саша, нельзя говорить "not big" в значении "небольшой" на английском. В этом случае лучше сказать "small." 

Haha, I think it is just common for native Russian speakers to say "not a big city."

Often I hear native russians speaking english and referring to things as "not so good."

My name is Sasha and I'm dying to speak in english haha:)

I live in a small city, and have been studying english a lot at my University.

Or maybe a 'medium-sized city', or possibly 'provincial city', but this has a certain other connotation (meaning). You would have to tell me what city you live in for me to give you the best descriptive adjective. Maybe even 'large town' would be the best words to use. 

My name is Sasha and I'm dying to speak in English haha:)

I live in a not big a small city, and have been studying English a lot at my University.

You're welcomed here

Abbas