"Gone to" means that you've traveled to some place and haven't returned yet.
Examples:
1. Sarika has gone to the supermarket. I wonder when will she come back?
2. Rohit has gone to France for the summer, so you can call again in September.

"Been to" means that you've traveled to some place and have already returned.
Examples:
1. Shakti has been to the supermarket. Now he's taking a shower.
2. Ali has been to Agra five times, so he is very familiar with it."