Any ideas to take a girl out during the day ?

DON'T go to the mall! How boring would that be for you!

Do something fun for both of you to make her laugh. I like mini-golf a lot. Then you can do lunch or coffee and/or go for a walk around like a park or your old high school where you met or something.

Make sure to keep it fun and lighthearted, especially on a "first date"-ish; that is the best way to get someone to fall for you again! Also, keep it relatively short; if it ends on a really good note then she'll definitely want to hang out again.

Good luck! Hope everything works out for you!

[PS and after you are back together, then you should do something romantic, like make a picnic. Even if it's cold, just have one inside somewhere.]

May I suggest that you take her to an art museum? It demonstrates that you have a bit of culture and, since you are surrounded by beauty (including your lady friend) there should be plenty to talk about.

As far as romance goes. if anything about the paintings or sculpture reminds you of your lady, be sure and mention it OUT LOUD! Romance is just doing and saying what the heart feels.

Movies, bowling, for a walk and crab some food. And at the mall you probably shop and just chat around, nothing much. And if want little bit of romance in this then buy her a one single rose. The most strong thing you can do at this moment is talk with her.

Though piece of advice. Be sure that she really cares for you. It might be only a momentum thing. She might gone already on a date but didin't go quite well and now she cries back to ex.
But that's only an example. What I am trying to say don't let love blind you. You will see things as you want them to see and make yourself believe in stuff. So be quite sure that she won't broke your heart again.

Fool me once shame on you, fool me twice shame on me.

Take care and good luck in love.