A drive out of town or away from Pak Meng is highly recommended.
You should go to the Khao Luang and Banthat mountain ranges where you will find plenty of water falls (such as Prai Sa Wan pictured in this blog), caves, trekking trails and relaxation.
There is also a botanical garden and as well as Khlong Lan Chan "non-hunting area", which is very tranquil and perfect for a picnic on the banks of a picturesque lake.
Of personal interest, I know that the Nature Adventure of Southern Thailand some years arranges a 4WD challenge.
It is an off-road "race" for members of off-road racing clubs in Thailand and from foreign countries, such as Malaysia, Singapore, Indonesia, etc., normally with more than 100 cars participating.
Lastly, Trang has a museum proudly showing the history of rubber in Thailand.
Trang was the first Thai province where rubber trees were planted. Governor Phraya Ratsadanupradit Mahison Phakdi brought rubber from Malaysia and planted it here before anywhere else in southern Thailand in 1899.