Our plan was to go from Heathrow to Paddington Station, buy our senior rail (discount) cards, book a hotel in Exeter, and then hop a train. Trying to 
Timbered building
buy tickets on the Heathrow Express, we couldn't get the self-service machine to work. Suddenly a woman appeared over our shoulder and advised us to select Heathrow Connect instead -- saving us about a third of the cost. When we still couldn't get the machine to take our credit card, she walked us through the program, patiently showing us which buttons to push. When we had achieved success she left us, pushing her cart full of cleaning supplies, returning to her job as a terminal cleaner. Our first taste of a wonderfully hospitable people!
At Paddington Station, we quickly acquired our discount cards each in a little blue case, and purchased tickets to Exeter on a mid-day train. Then we decided we should reserve a hotel room.
We had assumed we'd find a Tourist Office to help us, but the closest one was at Piccadilly Circus (we should have known that). After flailing around a bit, we found a company which offers hotel reservation services. Our clerk tried at least a half dozen hotels, with no luck - all booked up. As 
Mechanical clock
the minutes before our scheduled departure ticked past, he kept trying, but his choices either were too far from the station, or fully booked for that evening, or could only take us for one night -- forty minutes before train time he secured three nights (instead of the five we requested) at the City Gate Inn. Relieved to have someplace to stay, we enjoyed a speedy train trip to "The Southwest."
The walk from the railroad station to the City Gate Hotel was the toughest of any of our stops, from the station at Exeter St. David's, up a steep hill, around a corner and down a long street. City Gate's Address is simply Lower New Bridge Road. It turns out that New Bridge is a 19th century iron bridge spanning a steep hill. In the interest of thoroughness we walked down, then up, then looked across the street to see our hotel.
City Gate Hotel is recently remodeled and comfortable, although it is a two-flight climb to our room. We had delicious breakfasts and friendly conversations with the managers, and enjoyed staying in a three-hundred-year-old building.
During our first full day in Exeter we roamed the streets, admiring the decorations on the old buildings, where modern shops adjoin Tudor-era 
Exeter cathedral
buildings. This weekend is the final one for Exeter Heritage Open Days, an annual affair held in cities across the country where museums and historic buildings are open free of charge, and special concerts and lectures are given.
Walking to the Quai-side, along the River Exe, we descended a hill so steep that steps had been made (the street is named Stepcotes). We found the large mechanical clock where the king and two attendants gesture with their lances when the hour is struck. We're remembering that pub lunches can be very tasty, and lemonade is always available. We finished the day with a visit to the cathedral.
One of our first purchases at Waterstone's (the English Barnes and Noble) was a historical mystery novel, Dissolution, by C. J. Sansom. We're beginning to learn that we're interested in the Reformation -- possibly because the cathedrals in the cities we're visiting were the objects of the great reform, starting with Thomas Cromwell under Henry VIII and continuing through Oliver Cromwell, Thomas' great-great-great nephew.