My wife is from that part of the world, and we’re only 90 mins away so know it pretty well!
Great area for walking and biking as you’re slap between the Quantocks and Exmoor. From Minehead you’ve got direct access to some great trails / walks around North Hill, Bossington, Selworthy in one direction, and up above Dunster in the other. Both rideable from Watchet although I’d try and bypass the A39 if you can 😯
Quantocks are also within a very short drive – Staple Plain is a good kick off point. Get an OS map of the area and just make up your own routes, you won’t be disappointed.
Porlock and Porlock Weir are worth a visit – twee, but very pretty and quite interesting. Walk from Porlock to Culbone church in the woods is really nice.
Beaches aren’t great around Watchet / Minehead – still a bit murky from the estuary, but a drive down the A39 will get you to some lovely spots in North Devon (Woody Bay is nice for a dip).
The last bit of the drive down to Lynton / Lynmouth is particularly scenic and well worth doing on a nice day…. amazing views. The walk up to Watersmeet from Lynmouth is a really lovely stroll and you can extend it out onto the moor. Some good spots for river swimming further upstream.
Plenty of nice country pubs in the area too. Sure you’ll enjoy it.