Learn English – Ambiguity of “Lindsey told Jessica that she had cancer”

If you think about the word outstanding itself, you'd notice how it generally means "unique in a group of similar objects or people (stands out, get it?).

It thus can both refer to something that is not-yet-done (while it's supposed to be, because the group that it belongs to has mostly done stuff), but it can also refer to a certain positive quality of uniqueness.

For me, however, the common idiom seems to be to usually use outstanding to mean astonishing, great, impressive, unique, unless followed by something that explicitly implies a task-based logic:

This is outstanding work, Harry Potter! (surely means 'great work', not 'work to be done').

I'll make a list of some outstanding tasks. (one can argue that the speaker has great tasks to do, but he/she probably meant not-yet-done).

In the end, it's all about context. In your question:

What are some outstanding places?

it seems a bit awkward to assume either interpretation. I would've said:

What are some places you're planning to visit?

Or:

What are some places you haven't yet been to?

Or even:

What places are on top of your list?

But this is going outside the scope of your question.

You say that:

Mind you throughout the conversation flirtatious jabs were exchanged and she wished I was with her

This definitely influences the way that we should interpret the part that's confusing you. Let's take a look at what you said:

ME - Hope she gets better and you’ll never ever have to see me or that hospital again

You are expressing a wish, and two expected outcomes of that wish. The wish is that the girl's mother gets better. The expected outcomes are that a.) the girl won't have to see the hospital again b.) she won't have to see you again.

Now we can look at her response to that:

GIRL-Thanks. Hospital. Yeah. You. We’ll see about that :)

She is very likely expressing a wish to see you again in the future. Let's break up what she said.

First, she's thanking you for what I described as your wish above - that her mother will regain her health. Then, she's breaking up what you expressed as a single thought into two thoughts - you said "me or that hospital", lumping yourself with the hospital. She's now splitting "Hospital" on its own, separating it from you. So, that "Hospital. Yeah." is agreeing with your expected outcome of not having to see the hospital again.

Then she goes on to say "You. We'll see about that :)"

You said in your post that she said that she wished that you were with her. So what's she's saying with this is, after separating the hospital and you in your expected outcomes, she's saying that "We'll see about that :)" and disputing your expected outcome of not seeing you again. The smiley, which is a happy face, shows that she's not being pessimistic about her mother recovering, as @Shoe claims - if that were the case then a sad emoji would be appropriate.

So, all in all, everything points to her disputing your expected outcome of not seeing you after her mother is better, and is expressing a wish to see you again.