That is a long time for traveling from one place as a base. Consider dividing into two and do a home base twice.
A great place to do a base is the Cotswolds in England. We used Chipping Campden as a base for six nights (of course you need a rental car). The Volunteer Inn is a great Inn with spacious rooms at affordable prices. You can do the Cotswolds, Bath, Stonehenge, Avebury, Oxford, Stratford Upon Avon, Blenheim Palace and more.
There are many great places in Europe:
1) Strassbourg, France: From there you can visit the Alsace area of France, the Black Forest in Germany, some of the Rhineland, Switzerland.
2) Salzburg, Austria: you can visit Vienna, Berchtesgaden, Munich, more places in Southern Bavaria and Austria.
3) Tuscany, Italy: Siena or Florence. There are many great small towns and cities to see, including Pisa, Lucca, San Gimignano, Volterra, Lake Trasimene, and more.
4) Take a Greek Island cruise where your cruise ship is your base to visit ports on the mainland and its many islands.
5) Budapest: Take in that wonderful city and visit more places in Hungary as well as other nearby cities in Romania.