Yes, there is a $7 fee to enter the park or $35 for the annual Minnesota State Parks Pass. However, if you're up for a 15 minute walk you can park at the visitor center and avoid the fee.
There is a main lot by the visitor center, a small lot outside Lady Slipper Lodge, another small lot outside Lakeview Shelter, and a large lot passed the shelters near Lake Superior. Typically on a busy summer day there is also cars parked alongside the road inside the park.
Jonathan & I both have a great love for the outdoors, so it was important to us that the day was spent outside. We also, are fresh college graduates that needed an affordable option that would make our day feel special. Gooseberry Falls checked all our boxes. On top of that Duluth (and the north shore) has been a frequent vacation spot for Jonathan and I while attending MSUM and has become a special place for us.