If you have one week to spend in Sedgemoor, here are some suggestions:
It will take around 2-3 hours to climb up Glastonbury Tor and explore the ruins of the Abbey. There are also many shops and cafes to explore in Glastonbury town.
Cheddar Gorge is a natural wonder with stunning views and hiking trails. You can also explore the caves which will take around 1-2 hours.
Burnham-on-Sea has a long sandy beach, amusement park, and lighthouse. You can take a leisurely walk along the promenade and relax by the sea for an hour or two.
You can rent a bike and enjoy a scenic ride along the canal. It will take around 2-3 hours depending on how far you want to go. There are many pubs to stop at along the way.
Wells is home to the stunning Wells Cathedral, Bishop's Palace, and many independent shops and cafes. It will take around 2-3 hours to explore the town.
The museum has a huge collection of aircraft and exhibitions about naval aviation. It will take around 2-3 hours to explore.
There are many spas in the area to relax and unwind. Alternatively, if you're a golfer, there are many golf courses in the area as well.
As for places to stay, there are many options such as hotels, bed and breakfasts, and holiday rentals in and around Sedgemoor.