Location: Musical Hall - Nimbasa City
Like in Black & White, when you go to the Musical Hall and speak to the owner, he will give you a special prop, the Toy Cake prop. You can only receive this prop once, so if you received it through Memory Link, you won't be able to receive it here.
Location: All of Unova
Like in Black & White, when you go to a Pokémon Centre on your birthday, the nurse will stop you as you're going to give her your Pokémon and gives you a special birthday message asking if it's your birthday and thenwishing you a happy birthday. If you say no, she will state that she must have been mistaken.
Quiz - Icirrus City
Location: Icirrus City
New to Black 2 & White 2, there is a special quiz given by the people in Icirrus City on your birthday. It doesn't give any special items or anything, but mostly changes the dialogue.
Hope I helped! :)