What time of year do you have in mind? Also be aware that unless you own a week with excellent trading value, you may have a hard time getting any week in many European countries unless during the off season periods which can be undesirable.
If you are lucky enough to get a week at Sloane Gardens in the Chelsea section of London, this would be a great option. It is close to the tube (underground train), buses, stores, restaurants, and major tourist attractions. One can even get to and from the major airports by train, so no need to rent a car.
The San Francisco Exchange Company has good inventory for this small Victorian home turned timeshare.
Many European timeshares are located in the mountains or other remote areas and are difficult to get to, and far removed from the major cities. Europeans like to get out of the cities and go to rustic areas to relax and recharge their batteries, or to ski.
Also, I'm not sure about the age of your parents, but many European car rental companies will not rent to persons over age 70.
We have lots of friends in the 70's and 80's who vacation regularly all over the world, staying at timeshares. So if your parents are adventurous and in good health, there is no reason for them not to go. It is a great experience being exposed to the culture and history of foreign countries. We have stayed in timeshares in London, the British countryside, Paris, the south of France, east Germany, West Germany, Denmark, and Sweden and have loved everyone of them. While possible to reach them by bus, train, or taxi, we would not have had as nice an experience if we had not rented a car.