Hi, let me clarify few things first:
- there is an item literally called "gift" - it's main function is to increase relationship and decrease suspicion, you can buy it in the shop (not Peeptube shop)
- aside from those "gifts" there are items such as "numbing chapstick" or "suspicious lotion" that you can also give her and they make the night easier, some can be bought from the shop, other items drop from enemies
- then there are "accessories" - clothes and other stuff for Yuna to wear - those are purely cosmetic and can get bought from a vendor met during running at night, there are different items in the city and different on the beach
Ingredients for cooking can be bought from shop (not Peeptube shop) but you have to visit it everyday as they are rng