Vegas has a reputation for being some sort of scary place where you will get mugged and you have to watch your back 24/7 but that's not really true. Why? Because the Las Vegas Strip just might be the most heavily patrolled stretch of real estate in the world. It is very unlikely that someone will hold you up and take all your money as long as you are careful. So...you rarely have to worry about being safe in Las Vegas. But....if you want to be super careful, follow this advice.
The Las Vegas Strip, day or night, between at least the Wynn and the Mandalay Bay is arguably the safest street in the world. Not only are there LVPD wandering around everywhere, not only are their casino security guys looking for trouble at all hours of the day and night, but there are just so many people walking around that it is just a terrible place to try and commit a violent crime. That doesn't mean that someone couldn't pick your pocket while you are staring out on some casino or attraction but there are ways to deal with that. For one, stay aware. If you are going to get "wasted drunk," don't do it in the middle of the Strip. Just do it at your hotel or at a club and then take a cab "home." If you are carrying a fair amount of cash, maybe keep it in a money belt or in your front pocket or just keep one hand on your wallet at all times.
Downtown Las Vegas is also pretty safe, as long as you stay on Fremont Street under the canopy. But just don't be wandering off more than a block or two off the tourist areas. And, for God's sake, don't be trying to find hookers or drugs....that's how people end up arrested or dead.
Now, I'm a bit of a thrillseeker and I've probably wandered around to places I shouldn't over the years. But that doesn't mean that you should. If you want to be really careful, don't walk the Strip between the Stratosphere and downtown. You might be tempted but the people you will encounter are not usually tourists. You also might think that wandering up and down streets close the the Strip like Paradise or Industrial is OK. You will likely be fine but you are taking a bit of a risk. Most anywhere on Tropicana is sketchy and once you get east of Bally's on Flamingo, you might feel a little uncomfortable. Honestly, you should be just fine but, if you feel funny, it won't matter.
The other safety tip is to follow the same rules that you would follow anywhere else. Wandering around at 2 or 3 in the morning is going to increase your risk, whether it's in Las Vegas or Lawrence, KS. Honestly, if you keep your wits about you, you don't have much to worry about.