Trying to Write a Short Photo Caption and Description
You did very well translating it.

Some minor suggestion:


  "Caption: When I was in San Francisco's Chinatown" Translation: 当我在旧金山的唐人街


"When" indicates 'time', therefore, your translation should be 
"当我在旧金山唐人街的时候" (you can omit 当)


  Description: Last year, my cousin and I went to San Francisco's Chinatown. We ate Chinese food and drank boba milk tea. It was a great day! Translation: 去年我和我表姐一起去了旧金山的唐人街。我们吃了中国早餐，也喝了波霸奶茶。那天真不错！


"去年我和表姐一起去了旧金山的唐人街。我们在那里吃了中式早餐，还喝了波霸奶茶。真是不错的一天！"


the second 我 in 去年我和我表姐 can be omitted
我们(在那里)吃了中式早餐 
I suggest using 还(also) instead of 也(also/ too) in  "吃了中式早餐，还喝了波霸奶茶"。to indicate Boba milk tea is in addition of having Chinese breakfast (which is the main event).  
中国早餐  could mean "breakfast from China",  you should use 中式早餐  (Chinese breakfast) here, because you are in Chinatown, not in China
那天真不错！(sound too matter of fact, the day was good, but how good?) --> 真是愉快的一天！(describe your feeling about that specific day)