I would run to the supermarket, grab as many items of canned food as possible, then I would immediately locate a portable generator..... or maybe 10 portable generators, take them, grab fuel, grab books on mechanical repair, grab tools and find a fresh water source, like a lake or a river. I'd grab water filters, water purification tablets, a truckload of batteries and some guns for which to hunt with.
Without people, there's no one to run the power plants or the water system or grow food for you. That was one of the reasons I sorta hated Zombieland - if everyone's a zombie, how come there's power and water? Without maintenance, or automated systems, power would fail within days. If you're lucky, maybe a power plant could continue to churn out power for a few months, but it's unlikely. Without people, the only fresh water would be what's in the reservoir, and that could quickly go bad if you're not careful.
So the immediate priority would be to secure a portable generator. With care, and maintenance, you could make it last many years. Also, grab as much fuel as possible: coal, lighter fluid, gas, petrol, desiel, oil, wood, anything that can burn, pretty much. You're gonna need it, depending on where you live. Even in warm climates you'll need fuel to cook food or keep a fridge running.
Also, get a fishing rod. Learn to fish. That will be important.