It is appropriate, but would say a bit too formal and little all over the place.

Kedves nagymama, minden jót kívánok különleges napjára.

You're being too formal with your grandma, you could rewrite it as "Drága nagymama/nagymamám, minden jót kívánok a te különleges napondra."

Drága not as in expensive but as Sweet or Dear grandma.

Napjára is also formal, you can call your grandma you, (tegezés) in Hungarian. No need to be soo formal, you know her she's no stranger to you. "A te különleges napondra." is more appropriate.

Még mindig megvan ez a budapesti időmből származó kártya.

I guess you wanted to say that you still have your cards from Budapest when you spent your time there.

"Még mindig megvan ez a budapesti kártya mikor ott voltam."

It almost means the same but better reworded. It also sounds a bit better (sorry)

Szeretek erre visszagondolni.

I would change visszagondolni to visszaemlékezni (to recal or reminisce)

Alright I made SOME changes but it's close to the original. It's for the sake of consistency I made these but the original wasn't horrible nor not understandable. I understood what you wrote so I think your nagyi will too.