First of all to me that's actually looks like a response that shows interest from her side cause most people look at coffee date as something very casual while dinner dates got a more romantic vibes to it.
I would just invite her now to a bar close to your place since a bar is considered to be in the middle between casual (coffee) and fancy(dinner).
if she still insist on the dinner that's a bad sign and she's probably care about a kind of lifestyle
As a man who didn't get rich by paying for girls' dinners, my concern here is you've found someone who enjoys many dinners with many men at no expense to herself, either in terms of money or in terms of sex. Apart from Jay's options you also have "drinks after work at [some place], they've also got great bar food if one of us gets hungry". You have the best feel of this particular interaction and which option (if any) you should go with. Don't pick "expensive dinner", too hard to convert.
I usually tell girls I don't do dinner out for first dates and would rather due a coffee and go for a walk (near my place) or grab a drink (if I can't get them to come straight over).
Even cooking for them at your place is better then doing dinner out since you control how heavy or light the meal is and not like totally fuck up your chance to hook up after by her eating something that will make her lethargic
I would suggest cooking quesadillas if you are going to cook for her. They are easy / quick to make and pretty light. Add some chips and gauc or salsa on the side or veggie. Its a pretty light meal and you can easily do drinks with that type of food.

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I personally don't like coffee dates or dinner dates. I'd respond with "Funny coincidence. I don't do dinner dates. Let's just meet for drinks"