Thai people are generally pretty happy, but did you know that "Land of Smiles" refers to the number of smile-types found here (I believe it's 37) and not the mood of the Thais?
Sounds random, I know, but I first read this on a placard at the airport in Trang, a far-southern province that's extremely underrated. Its islands all bear some amazing accolade, from Koh Kradan (deserted), to Koh Mook (home to the aptly-named Emerald Cave), to Koh Libong (also deserted but bigger than Kradan, which means more opportunities for discovery).
A word of caution, however. While other parts of Thailand's lower Andaman region are lovely (hello, Ranong!), some are past their prime. Namely Koh Lipe, a proto-Phuket whose biggest attraction these days is the single-boat journey you can take to Malaysia's Langkawi Island from there.
The islands of the Gulf of Thailand tend to get the short stick for many travellers, and not without reason. After all, Koh Phagnan is famous for its Full Moon Parties and Koh Samui for its exclusivity. While beautiful, however, they simply can't compete with the dramatic, fluorescent waters and towering limestone karsts of the Andaman islands.
On the other hand, the eastern reaches of the Gulf of Thailand might be worth a closer look if you don't have a long time to escape Bangkok. In fact, Koh Mak (part of the Trat archipelago) was the first Thai island I ever visited, and its palm forests reminded me of the best beaches in Goa, India. Nearby Koh Kood, Koh Wai and even busy Koh Chang are also amazing, although I'd avoid buying into the hype that Koh Samet (which is technically the closest "good" island to Bangkok) is worth visiting.
If your Southern Thailand priority is more about authenticity than beach-going (and, to be sure, you speak some Thai or can quickly learn it), an alternative destination would be the city and province of Nakhon Si Thammarat. Here, you can not only marvel at the towering Buddhist City Pillar shrine, but explore Southern Thailand's Muslim heritage at the city's Salahuddin Mosque and Panead Road Night Market (Halal Food!), to say nothing of the utter lack of tourists you'll enjoy.