What does "That sounds quite a day" mean?
- That sounds quite a day! You're going to have a good time.
- Yes, you're right. We really are going to enjoy it.

Question

Answer

It should actually be written, 
That sounds like quite a day.
The meaning here is that the day this person has planned is full of a lot of things, and from the context here,  a lot of positive things.
This is a pretty common phrase to describe that your day was busy/eventful/full. It could be positive or negative.
'It's been quite a day...' 'Oh no, what happened?'
"It's been quite a day, hasn't it?' 'It sure has! What a great day.'
Hope this helps you out.

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