This is Punta de Choros inlet and the Humbolt Penguins National Reserve:
If you’ve got no car, there are two possible ways to get here: the cheap one and the expensive one.
The expensive one is obviously the most comfortable choice. You hire a tour agency, they pick you up early in the morning at your hotel/hostel/whatever door, and drive you to Punta de Choros, where they’ll do all the paperwork and stuff to get you on a boat, and if possible, disembark on Isla Damas, for around 44000 CLP per person.
But you also have the cheap option, which, to be fair, is not really uncomfortable, but you’ll have to do it all by yourself.
If you are still interested, these are the instructions to get to Punta de Choros from La Serena:
There is a bakery on Francisco de Aguirre Avenue and Matta Street, called Los Griegos. Right outside the bakery, two buses leave to Punta de Choros at 8:30 am and then, at 9 am, every day, for 4500 CLP.
It is important to book both tickets as soon as you get to Punta de Choros, since you might be in the queue for an hour.
The tour itself can take from an hour and a half to three hours, depending on whether you are visiting Isla Damas or not, or if you are hiring a private tour once in Punta de Choros.
If you still have time when the tour is done, you can have lunch at the small restaurants around the (also small) touristic installations. Main courses go from 6000 CLP, but they have no vegetarian or vegan options.
Buses will start arriving to Punta de Choros inlet again at about 3:30 and will take you back to La Serena in an hour more or less.