16 days is not enough to get a grasp of what Europe has to offer. You must decide what you want: warmer countries, beaches, history, culture, gastronomy etc. I think Germany (Berlin, Frankfurt, Munich) is a good start point. Also, you could think of France, not Paris in particularly, but maybe Provence or the Loire valley. The countryside in France is extremely picturesque and quiet and can make a great destination for 2 aged persons.
Its awesome to see that you want to travel on your own. Thats probably the best way to travel where you are not bound by an itinerary!
I have been to a couple of countries in Europe, namely Germany, Austria, London, Ireland and I must share that their public transport system is state of the art. The trains, subways, buses, trams are all connected seamlessly.
Also, as soon as you reach, you can visit the tourist information centre where a map of the place is available. That acts as a handy guide to the places to visit and the route as well
If you would like a first hand experience of what some traveller's did while on their holiday, here is an interesting link I found. Sharing the same:
Will be glad to help with any other tips on the countries I have visited.
[ Edit: Sorry, no promos please. ]