October 9th, 1961 was a day never forgotten in my household.
I don't know if it's grammatically incorrect, but I suggest you don't begin a sentence with a date; it's weird. Perhaps, something like:
The morning of October 9th, 1961 radiated with exuberant smiles and warm feelings; a day never forgotten in my household. It was the day Uganda...Each year, this day stands as a significant remembrance, one that will never allow to me to forget my Ugandan roots.
"Roots" didn't sound too fitting. Maybe use the word "heritage" instead.
My grandmother prepares a variety of delicacies, ones that make any person salivate
Again, vocabulary choice. "Salivate" sound too scientific and doesn't give off that home-y feelings radiating from your grandma's food.
Being a first generation American, I enjoy embracing my cultural background with hopes of bringing my unique ingredient to the already simmering American melting pot.
I think you meant the "2nd generation" instead. Your parents would be the first generation of Ugandan-American
Overall, I like the descriptions of the family activities you do on that day, but I would suggest that you elaborate more on how these activities helps connect you to the Ugandan culture or how this culture had affected you.
Good luck :)
Take my correction as suggestions.