Session Prep/ Improv Help

Hello there! I’m a first time DM and am currently running a campaign with 4 friends. And while for the most part it’s going great, I am having some issues with actually prepping for sessions and doing improv.

See, my issue with session prepping so far has been more so having to do with actual story and not being prepared enough. For context, my campaign takes place in one city, a tropical island resort town designed to be perfect year round. The weather from the temperature, too the humidity, and even the breeze have all been perfectly engineered to make this the perfect paradise on earth. And there’s no shortage of things to do either, with luxury shops, hotels, and a casino. I also have a class divide, with a more impoverished area of town that is conveniently avoided by all of the nobles that visit for vacation.

Now, my issue with story currently is knowing where to actually take it. The next location, the next quest. Now, so far, I have had my players help dictate that course of action as in a real story, the main character decides where they go and what they do. I have only been offering minor guidance on where they need to go and do. But, sometimes, I have absolutely no idea where to take the story and that’s where my issue with improv comes in. My improv skills aren’t completely terrible, I can get a somewhat coherent story. BUT, a lot of times what I say when I improv locations and people aren’t that great, and sometimes don’t really make sense for what’s going on.

So, my main question, is how can I session prep to be more prepared, but also improve my improv skills so that when I don’t have enough prepped, I can improve and make the story more coherent and entertaining for my players?