Taunton is the main county town near beautiful West Somerset and Exmoor, but not a worthwhile tourist attraction compared to Bristol or Exeter.
Hitchhiking at Junction 25 on the M5 Taunton is 2 miles east of centre and both Northbound and Southbound sliproads are very busy in the daytime, and have enough length for cars to stop. Hence 25 is the best M5 junction for hitching in Somerset.
Otherwise, the service stations at Sedgemoor (Highbridge) and Taunton Deane (Wellington) are good spots and directly on the M5. If you are heading far into the south-west, it is a very good idea to get to a service station and display a sign: "A38 Plymouth Please" , or "A30 Cornwall".
Those two service stations, Sedgemoor (22) and Taunton Deane (26), get very quiet after 19:00, so expect a 1-2 hour wait .... and also difficult in high summer due to very heavy tourist traffic and caravans