Delfino Plaza has probably the easiest 100-coin Shine in the game, since you don’t really have to do much to get it. There’s two possible methods in obtaining the Shine, but the second method requires you to have access to [Corona Mountain], while the first method can be done as soon as you gain access to the plaza.
The method that unlocks as soon as you have access to Delfino Plaza will have you journeying through the sewers to get the majority of the coins. The sewers can be a bit of a maze, but it’s not too bad. The ideal starting point would be the manhole cover right by the entrance to Bianco Hills. Once you’re in the sewers, you will get a top-down view, so move north to a four-way intersection, then continue north to a bigger area, where you will find nine coins (9). There will be another big area to the north of the first, where you will find another nine coins (18). Return to the 4-way intersection and head west, then north when you can, collecting nine more coins (27).
Backtrack and head east at the intersection, where you will come to another split in the path. Go south to find another area with nine coins (36), then return to split and head straight north. Upon getting to the corner, move westward and look for the opening to the north, leading to two large areas with two sets of nine coins each (54). Back down to the main path, continue west and the path leading north will have another ten coins (64). That’s all of the coins in this section of the sewers, so take any of the manholes back to the surface.
In the one corner of Delfino Plaza, where the cannon that shoots you to Pinna Park, drop back down into the sewers and follow the trail south for nine more coins (73). Pop back to the surface and look for the manhole nearby that is on a ledge near the previous cannon, requiring you to jump/hover to it. This manhole will take you to a different set of tunnels in the sewers, leading to two more sets of nine coins each (91). There is one more set of coins in the sewers, but it’s via a hidden manhole on the beach, next to the vacant umbrella. You can see a glint of it sometimes while running around, but you will find eight more coins in this little area (99).
So, that will leave you with 99 coins and you only need to grab one more. In fact, there will be six coins underwater right by the last manhole/umbrellas on the beach (105). There are also various Wanted posters around town, that you can spray with FLUDD, most of which will yield a single coin. The Shine will spawn on a platform out in the sea that is a little too high to normally get to by jumping out of the water. However, there is a boat that circles it, so wait nearby and jump on the boat, then hop off to collect the Shine when you get close enough.
If you don’t feel like diving into the sewers to grab all of those coins, then you will have to wait until you have access to Corona Mountain. Once you do, there will be a Pianta by the boathouse you can pay 10 coins to in order to return to Delfino Airstrip. There’s not really much to say about the airstrip, but there’s a lot of coins here. Whenever you’ve collected 100 coins, then you will find the Shine on top of a little water tower.