When we were trying to figure out where to take our honeymoon, I struggled to find real experiences of couples who tried traveling to Puerto Rico with the K1 visa. The only comments were people warning against it, but none that had actually tried it, so I thought I would share my experience here in case it is helpful to others.
After our wedding, we took a direct flight from Baltimore, MD to San Juan, Puerto Rico. We had absolutely no issues and spent a wonderful vacation on the beach and in the rain forest. He travelled on his passport and I just used my driver's license as identification. The only time anyone looked at his passport was during the check-in (just to confirm identity and that the name on the luggage tags was correct) and when going through security, again to confirm identity. He says the TSA agent during the return from Puerto Rico to MD did flip to the visa page with his K1 visa, but asked no questions about it.
It was the same process as any other domestic US travel. The only difference was the agriculture check of bags when leaving Puerto Rico (no identity documents checked at this time).
The primary concerns I heard were that:
Going to Puerto Rico would be considered leaving the US (it's not - it's definitely part of the US and a flies out of the domestic terminal at the airport)
Immigration could stop him at the airport and give him a hard time (didn't happen and he had all his paper work in place)
We could risk being out of status if the flight had to make an emergency stop in another country (I realized this risk would be no higher than the risk of emergency landing in Canada on a flight to Michigan and if we did, I don't think we would be sent through immigration - I didn't even have my passport with me to be able to pass immigration in another country myself).
Everyone has their own risk tolerance, but my personal conclusion is that this risk is extremely low. Would highly recommend Puerto Rico for anyone looking for a beautiful honeymoon destination!