"Still" as an adverb usually comes after the BE, or, auxiliary verb and before the main verb. "I am still going to the store." "Going" is the main verb. Sometimes "still" can come before the BE verb. "I still am going to the store." To me this sounds funny but it is not wrong to say. It makes it feel like you are still going even though maybe something happened that made it hard for you to go. "Still" can even come at the beginning of the sentence sometimes. "I don't like how much my job pays me. Still, I'm grateful I have a job at all." "Still" here is more like "however" or "although." This makes it feel like a contrasting sentence.

1. Do you still go to the gym? (slight more emphasis, I guess) = Do you go to the gym still? (neutral sounding) 2. I'm still hungry! (emphasis) 3. I don't care what you say! I'm still going on my trip to NYC! (contrast/emphasis) 4. I've corrected him many times, but he still makes the same mistake. (contrast) 5. I know I am not invited, but I'd still like to come to the party. (contrast) 6. I can't right now because I'm still working. (contrast)