Why not? It looks like a "best European capitals" tour. It will be doable if you fly between cities (only Paris-London will be doable by train).

For each of the four capital cities, you should be prepared to walk a lot in order to get impressions of the cityscapes and the monumental buildings. Otherwise, you find tons of worldclass museums in each city, cathedrals, palaces and entertainment. It will be up to your tastes what to select.

Here are just a few personal favourites:

- London is the only city (of your selection) where you have a chance to visit inhabitated Royal palaces. Visit either Buckingham Palace or Windsor Castle (which I find more impressive, but it's a bit outside) or both. Of course, you should see the Tower (early in the morning, just after opening, the crowds are bearable) and the Houses of Parliament. I would also think about a daytrip to Oxford which is a very special place. The train ride takes just one hour from Paddington Station.

- In Berlin, the Pergamon Museum is outstanding, because it displays huge ancient buildings, especially a gate and procession street from Babylon. Stroll along Unter den Linden (or take the public bus 100, which offers excellent sightseeing for a nominal fare), walk over Oranienburger Straße at night, explore the nightlife which is best among the four cities.

- Rome is famous for Roman heritage (the Forum Romanum is a must) and baroque churches. I would follow Roman traces - the Forum, the Pantheon, maybe the catacombs. Also the Vatican and its museum is special. For a side trip, Ostia Antica and/or Tivoli are interesting.

- Paris boast grand boulevards, squares (Place de la Concorde is most famous) and monumental buildings. Explore the city just be walking. A side trip to Versailles is most rewarding.

Since you selected these cities and indicate that you have been to Europe before, you must already have some idea of what to see in these places and what you found "special". Nonetheless, not having any idea of your interests, my best advice is to run to your local library and/or bookstore and pick up some guidebooks that cover these cities. A general guidebook such as "Fodor's Essential Europe" is going to include the highlights and "must sees" of these 4 cities.

Agree, get a good guide book - like the Top 10 London, Paris, Rome, Berlin and see what the top sites are. Pick your favs.

Be sure to book your Eurostar between London and Paris as soon as you can to get the cheapest rate.

Also I would fly into say Berlin, fly into London, Train to Paris, fly to Rome and then fly home from Rome to avoid wasting time and money backtracking.

I would personally pick 2 of the 4 and take more time seeing them but thats just me. I hate spending alot of time and money on transit during my vacations.