Whether or not a hotel room is "notoriously unsafe" will vary wildly from hotel to hotel, but I'd be hard pressed to imagine one that is less safe for your valuables than a beach.
If your room has a safe, use that.
Otherwise, keep your passport out of sight (not just sitting on the desk) in your room.
You might need your passport to make certain purchases that require ID
(alcohol if you're in your 20s, pseudo-ephedrine decongestants, etc), but not just to walk around or to be on the beach.
Leave your passport and most valuables safely behind when you go to the beach for the day.
travel.stackexchange.com/users/46/Kate Gregory
I do not think the U.S. requires foreigners to carry passports with them.
Unless you travel near the U.S.-Mexican border, virtually no one will check your passport.
You can put them in your room safe.
If you travel close to (meaning anywhere 100 miles/161km from) the U.S.-Mexican border, it is in your interest to carry your passport with you.
CBP and ICE USBP officers carry out random checks here and are known to detain (quite arbitrarily) individuals that they believe might be "illegal immigrants".
That said, if you have any plans to drink, you might want to show your ID.
Some U.S. establishments can be really strict, and might ID-check those who are apparently 21+.
travel.stackexchange.com/users/55892/xuq01
As others have said, your hotel room safe is your best option that will be widely available.
Almost all hotels have them.
The more respectable hotels will definitely have one.
Even some Airbnbs will have one.
You will not need to have it on you for regular use while walking around.
Unless you are suspected of breaking the law, police will not require it of you.
So, why risk loposing it (through your own fault even) by carrying it.
If you are driving in the U.S.
the passport is not enough to be legal.
You actually need to be able to show your drivers license.
Now if the worst case scenario happens (you lose it, the hotel burns down,
it’s stolen), it is better to have taken precautions.
The first of which is to keep copies of you travel documents where you and only you can access them.
Maybe giving copies to a trusted family member could work.
At the very least, they can help you in recovering duplicates.
Or, they can send you the copies by fax or some other means in a pinch.
Most importantly, let your embassy know you will be traveling in the U.S. before you leave home.
That way, someone knows where you are or should be.
travel.stackexchange.com/users/108254/Dean F.
Most hotels have room safes.
I can’t remember the last hotel I stayed at that didn’t have a room safe.
Even though these room safes are notoriously easy to break into (often just a magnet is enough), it’s still safer than the beach.
The front desk of the hotel may have a separate safe.
If they do, they take responsibility for the contents.
The one place I would absolutely not trust is the lockers in youth hostels.
travel.stackexchange.com/users/17153/RoboKaren
Some hotels have a facility to keep your passport in their own safe custody .
Please check with the front desk .
For moving around you can carry a scanned copy of your passport on yoir phone and any other supplementary identification card like your Driving license with you.
travel.stackexchange.com/users/90900/Atmanirbhar Bharat
I have been told in the past that while in the United States I must always carry my passport with me, and I have been stopped at least once by Border Patrol officers (while already in the US) and been asked to show my passport.
I do not know what might have happened if I did not have it on me.
Doing a bit of searching online, I found Do I Need to Carry Documents While I’m in the USA?
which seems to indicate that it is required for all foreigners to carry their passport (or immigration documentation) on them at all times.
You may want to invest in a small water-proof sealed bag or container that you can attach to you while swimming (rather than having the risk of losing it or having it stolen if you leave it on the beach...)
travel.stackexchange.com/users/40422/Midavalo
If I was going swimming I'd consider a hotel safe as others have said. For all activities that did not require me to "lose control over my clothes"
I would (and always do) carry my passport with me at all times.
I use a small "purse" with a neck cord that is designed to fit a passport and a few other non-bulky items (eg VISA card and a number of $100 or equivalent notes.
I wear this with the strap adjusted
so it hangs inside my shirt and with one end straddling my trouser belt line.
There it is comfortable, location-invisible and even if someone knew it was there, exceeding-hard to access without me noticing.
On numerous international trips this has always been "hassle free".
YMMV -
but, probably not.
In my own country when visiting a beach to swim, I carry a minimum of valuable down to the beach.
I place car-keys and anything else valuable in a small plastic bag and surreptitiously bury this in the sand in an inobvious manner under my beach towel.
The main hazard is the potential to remember to recover it when I dress and leave :-).
travel.stackexchange.com/users/3301/Russell McMahon
You are not looking for a 100% secure, bullet-proof way to store your passport, but for the best option available to you.
And then you weigh in convenience
et voilà, the hotel room or front desk usually wins.
If you are feeling paranoid, keep it somewhere where noone would bother to look and staff cleaning your room won't accidentally throw it away.
As a precaution against loss of your passport in general, theft or otherwise, you should have printed copies of your passport at various locations, such as your backpack, wallet etc.
Nowadays, you should also have a PDF or image of it at a secure cloud hosting service.
travel.stackexchange.com/users/85676/knallfrosch
In the USA, what would be the best practice to keep my passport safe when I go e.g. to the beach for a day trip?  I'm worried that I might easily lose it on the beach (Solo traveller). On the other hand, a hotel room seems notoriously unsafe IMHO and I think as a visitor to the USA, I am required to carry a passport. Does CBP require this in all states?
Where to store passport during day trip in foreign country
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<usa><passports><international-travel><security>
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travel.stackexchange.com/users/83828/stephanmg
Leaving your passport in the hotel room safe is likely to be safer than taking it to the beach. You could also leave your passport at the front desk of the hotel. A hotel is generally safer than a beach, you can use a room safe or leave your passport with the front desk.
Your room is likely safer than a beach. The hotel room safe is a good option most of the time. Hotels can look after your passport at the front desk.#