[M/F 24] Is this a bad first date idea

Getting drinks with a girl in the city that I’ve never met. My idea is to suggest this rooftop bar that is rather fancy/expensive, where we can get a top notch cocktail. Then there is a sports bar down the street that we can pivot to if we want to get more drinks.

I don’t want to get more than one round at the rooftop bar because its pretty expensive and seems like a bit much for a first date. But also not sure if suggesting bar hopping is a great idea. I might end up just suggesting the sports bar. What do YOU think I should do?