Should I make my domain name something like energydrinks[dot]com and then optimize my pages like energydrinks[dot]com/energy-drinks-new-york. Or would I have an easier time just buying multiple domains instead? I'm especially interested about this since I want to target cities.
well, the domains you're probably going to want are definitely gone, so you can probably forget trying to gain a boost for SEO based on the domain name. Your article titles can have an impact as you have indicated, but you are entering a very competitive niche, and have some major competition.
Create cities specific landing pages like "energydrinks[dot]com/energy-drinks-new-york". This will help you lot. Make sure you will navigate these pages from home page.
I will not suggest for the multiple domains, instead of this, try to get the single domain name having specific keyword and then optimize the sub-pages which are targeted for different cities. Also optimize the url of those pages as you have mentioned.
buying multiple domains and re-directing them is absolutely useless. instead, optimize the URL and pages of your site to target the various cities