Naps are a betch's best friend, other than Moscow Mules and her actual best friend. Why limit napping to just home in your bed? Much like running into your ex, you never know when you're going to be sleepy, so you should just always be prepared.
The first step to napping in public is to ask yourself, would someone think I'm homeless? If the answer is yes, like if you're on a random sidewalk, then probably not a great time to take a nap. The harder to get into the establishment is, the better candidate it is for a nap. For example, napping in a club is a good way to say "hey I'm a little bored so I'm going to entertain myself with my own dreams until things get interesting again." If you end up in the White House, for example, you should definitely take a nap.
Depending on the time of day, there are different strategies to getting away with napping in public. If it's the day, you can sneak in a nap in a park, as long as you're surrounded by other people in the park that look like they probably have jobs. Sleeping on a patch of grass is really not that different from sleeping on a sidewalk, but it's much more acceptable and you can take advantage of this. While families play frisbee with their dogs and children, you can easily nap undetected nearby. In a park or on a beach, it's totally viable that you might just be listening to music and tanning. Keep your headphones on, put some sunglasses on, and you can nap for hours without anyone bothering you.
If you have no access to a park, find the most expensive pourover coffee shop in your neighborhood and set up your computer like you're about to work on your novel. Then put those sunglasses and headphones on, and you can nap for hours with your head propped up in your hands without anyone bothering you. You can also get away with casual napping at a bookstore, if you can't find a coffee shop.
If it's night time, you want to nap around as many friends as possible. For example, you'd never want to nap by yourself on a bar stool because that's just sad. But if you're at a table in a bar with 8 of your friends, then nap away. You're in a cab alone? Don't fall asleep, fucking duh. There's 5 of you packed into an Uber meant for 4? Announce "wake me up when we get there I need a nap" and go to sleep before anyone can protest.
The one thing you should remember when napping in public is the nicer you look, the easier it will be. Look, you really believe Disney princesses were always cast into spells? They were just fucking tired all the time and wanted to nap. The nicer the place, the better the nap, with the exception of a hotel lobby. Like, just get a room at that point, you're embarrassing yourself.