Seeing you in that red dress reminds me a lot ___ our honeymoon. Do you remember that red dress you bought in Hawaii and you wore it nearly every day!
Why is "of" the correct answer?
In most languages (I don't know many languages, but I think it's the case) there is a thing called collocation, which are words that fit best when put together with other specific words. It's a grammar rule which, in formal language, cannot be broken. In English, for the verb to remind we have many collocations, with adverbs, other verbs and prepositions.
For prepositions we have two options only: of and about
When we want to talk about something that will happen, we use about:
I rang to remind him about the party.
When we want to talk about something that happened in the past or something that is known by the person we're talking to, we use of:
She reminds me of my first teacher.
In your case of is more appropriate because it is something that happened in the past:
Seeing you in that red dress reminds me a lot of our honeymoon.
"To" is also a possible preposition to use together with remind, but then it has a similar meaning as "about", in the sense of talking about something that will happen or something that happens frequently but we need to trigger our memories to do it:
She reminded me to take my medicine in the morning.