Within this time-frame I suggest the following:
- 3 days in Hamburg. Plenty to see near the harbor, great Portuguese restaurants there, very relaxing city.
- 3 days in Berlin. Go see some of the historical sites, explore some of the new areas
- 3 days in Vienna. Very nice city, great architecture.
- 1 full day in Venice. Historical city is not that big, you can come in the morning via train from Vienna, and leave with an overnight train to Rome
- 3 days in Rome. One of the greatest cities in the world, plenty to see.
- 2 days in Milan.
- 3-5 days in Cannes and Monte Carlo. It's your honeymoon . You can find some affordable hotels there, but in my view it's a must-do for this trip.
- overnight train or flight to Barcelona, where you can spend 3 days there, before catching a low-cost to UK.

Greece in my view it's over-rated, compared to some of the places above.