No. You legally cannot do this right now
As of today, San Diego is under a regional stay-at-home order, which means that travelers must quarantine after arrival before they go anywhere else in the state.
This is laid out in an information page breaking out stay-at-home orders by region. San Diego is in the Southern California region, marked as being subject to a stay-at-home order right now.
The regional stay-at-home orders impose a variety of restrictions, and the one most relevant to your question is item 3:
- Except as otherwise required by law, no hotel or lodging entity in California shall
accept or honor out of state reservations for non-essential travel, unless the
reservation is for at least the minimum time period required for quarantine and
the persons identified in the reservation will quarantine in the hotel or lodging
entity until after that time period has expired.
This doesn't guarantee that a hotel will not take your reservation for a three-day stay, but it does mean that a hotel will be breaking the law by doing so. Even if a hotel does take a reservation for your proposed three-day visit, that does not protect you from consequences for any laws you may be breaking yourself.
You can't camp either:
g. To promote and protect the physical and mental well-being of people in
California, outdoor recreation facilities may continue to operate. Those
facilities may not sell food or drink for on-site consumption. Overnight stays at campgrounds are not permitted
Exploring San Diego is also a pretty clear violation of the stay-at-home orders.
The relevant laws under which the order was issued are listed there as well:
10.This order is issued pursuant to Health and Safety Code sections 120125,
120130(c), 120135, 120140, 120145, 120175,120195 and 131080; EO N-60-20,
N-25-20, and other authority provided for under the Emergency Services Act; and
other applicable law.
Conditions might loosen, even relatively soon (though I wouldn't bet on it). I don't know when the Southern California region's stay-at-home order began, so it's possible that it could expire in the near-to-moderate future. Calling the California Department of Public Health (CDPH) could get you more information (though they won't be open today, as you discovered, due to it being a holiday). But for right now the answer to whether or not you can travel there for a leisure vacation is an unambiguous "no".
If you choose to travel to California anyhow, and refuse to quarantine, you may or may not be caught
It's obviously not impossible to break the law without being caught. If monitoring of travelers is lax, it's entirely possible that you could violate the restrictions without immediate consequence. Monitoring could also be retrospective: you're unlikely to be able to get a hotel room without a credit card, for example, and so there would be a record of where you stayed and for how long. An airline would certainly have records of your flights.
A question on Law.SE can get you better answers about how the current COVID restrictions are actually applied, and what risks you may face (if any) from different approaches to your proposed vacation. I have found many posters there with deep knowledge of legal situations in specific states, and they can probably get you very precise information, from a legal perspective, on what you're asking.
You would be putting yourself and others at risk by traveling to California right now
I'm not interested in giving a full explanation of absolute and relative risks here, so I'll give a quick summary instead: CA has one of the worst COVID outbreaks in the country right now. If you are infected and contagious while there, you could make that problem worse by infecting California residents. If you are injured, or become sick with something (COVID or otherwise) and require an ICU bed, you will be taking up scarce resources which the entire stay-at-home order is meant to preserve for California residents.
Finally, traveling to a place where COVID transmission is rampant increases the likelihood that you will become infected while there and then you could bring the disease back to your home, potentially causing (or exacerbating) the COVID situation there.
To head off any "but I'll be careful while there"-style arguments, intending to travel to CA right now and not only specifically not quarantine but also explore the city strongly suggests that you will not, in fact, be sufficiently careful. If you're willing to disregard the laws and guidance around out-of-state travel simply due to restlessness and being tired of Winter, it suggests that you might be a bit loose with other guidelines as well.
I sympathize. Really, I do-- I'd love to travel right now. My grandmother's funeral is this Saturday, and I won't be able to be there due to travel restrictions. But the restrictions exist to limit the spread of COVID, as well as the consequences of rising infection rates.
This is one of the most dangerous times during the entire pandemic to travel within the US, especially by air, and California is one of the most dangerous places in the US that you could travel to (as far as COVID is concerned). If you really fell you must travel somewhere in the immediate future, finding someplace you could drive to that is suffering a less intense outbreak is a much safer and more defensible option.