I want to know if this is doable...

I want to spend 40-60 days travelling and here is what I have come up with so far.
As well please leave me suggestions of your favorite European cities and things to do I have never been! I'm interested in sight seeing that has to do with art and history/architecture
Thanks!

1 day fly there
London: 3 days
Paris: 3 days
Belgium:4 days
Amsterdam: 4 days
Berlin: 3 days
Prague: 4 days
Vienna: 4 days
Budapest: 3 days
Belgrade: 2 days
Greece: 1 week
Italy: 1 week
Spain: 4 days
1 day fly back

Remember that it takes 4 nights in a place to get three full days. And you have listed a week for Italy and Greece, both places where you could spend a month. Do you know what you want to do/see/experience in these countries? List the things, figuring in transport time and see if it is realistic.

Me (or anyone else) else telling you what our favorite destinations are will not help you.

I can say that I've never spent less than a full week in London; I've been there multiple times and will return.

I'd suggest you cut your destinations by half.

You haven't said anything about budget, but you are covering a lot of territory, and moving every few days, which will make your trip much more expensive than it needs to be.

Spend time with guidebooks and see what places appeal to you most.

It's "doable" but not likely a very popular plan with many people here...

IMO, it feels like you've randomly assigned a number of days to these destinations without much regard for the amount of art, history and architecture in each and how much time you'd need to see what you want to see there. A week for all of Italy is particularly puzzling. And I'm guessing you haven't taken into account that most museums and many sights aren't open every day.

What time of year? Some of these places in the hottest days of summer might need more days because the heat and/or humidity could slow you down.

Some places seem to be chosen at random. I am guessing there must be some special thing you wish to see in some of them.

The allotment of time in different places seems also to be random. For example, you gave a major city (London) less time than Prague. If you arrive in London, you will be jet lagged and should allow an extra day to recover. You give 4 days to the city of Prague, only 4 days to the whole country of Spain and only 7 days to the whole country of Italy, which some say contains 40% of all art in Western Europe.

You must allow for travel time, about 1/2 day (or more) when you move from one place to another. To get 3 days in a place, you must spend 4 nights.

Spend less time traveling from place to place, so you can actually see more.
With an interest in Art, History and Architecture, why not make a list of some of the great sites you do not want to miss. Then extend that to include other nearby sites of interest. Example: Sagrada Familia in Barcelona, Spain. Spend 3 or 4 days in Barcelona and see other works by Gaudi, plus Palau de Musica. Take a short, cheap flight to Granada to see The Alhambra, then Sevilla and Córdoba and Madrid for the Palace. Daytrip to Toledo for the magnificent Cathedral., etc.

You can work out the real iitinerary later, but to help you now get a grip on planning.
Lay it out with important sights.
Day 1 depart home
Day 2, arrive London, walking tour, see Norte Dame
Day 3, 4, 5, London, museums, churches, walks, West Minster, canal boat Ride, Tower Bridge, etc.
Day 6, travel to Paris,
Day 7, 8, 9, Paris, museums, walks, the Louvre, etc. Put in anything on your must see list.
Day 10, travel to Amsterdam
Day 11, 12, 13, Amsterdam, tour Anne Frank House and Van Gogh Museum, Rijks museum, trip to see windmills and landscape. Short trip by train to see Haarlem, Delft, etc.
Day 14. travel to ?
Day 15 & 16 tour?
Day 17, travel to?

Its doable but very hard work. I have a feeling that by the end of the trip you will have covered a lot of ground but not seen very much of anything. It will all have merged into a blur and you won't remember much about anywhere....

Sure you could do that, but why would anyone want to? It's incredibly random and very rushed. Do you run around like this when you're home? If art and history and architecture are your main goals, you should cut down your destinations by half and take advantage of the wonderful offerings of a few big cities (not to mention places that are NOT big cities, which you haven't even touched upon - Europe is not just big cities and there is art and architecture everywhere).

too many sites and too many second class cities in with world class cities.

I'd drop Belgrade and probably Spain (you can see nothing in 4 days so why bother), then Belgium can go, lovely place but nah.

That frees up 10 days, stick 4 in London, 2 in Paris an 4 in Italy.

What time of year, makes a big difference in Greece?

Trains? For all cities the best way - for lots on trains check www.seat61.com; www.budgeteuropetravel.com and www.ricksteves.com. And with that many trains check into railpassses. But yes need to cut back a bit and spend more time in London and Paris, etc. Figure one day travel between cities.

It does sort of appear you have just taken a list of random cities and tacked on 3 countries at the end.

Unless we know more about why you chose these places it is difficult to help must (or advise which to cut out -- you do need to cut several)

London is the largest city (by far) in western Europe and has masses of art/history/Architecture - and you have given it 2.5 days, the same as Berlin and less than Vienna. It may sound brutal but if you are only allowing 2.5 days for London you are better off skipping it.

You will get off each train or plane in a new city, have to acclimate yourself to new surroundings, and barely find your way around before you are jumping on the next train/plane.

You can't 'do' a country in a week - but you can see a couple of cities in a country so you need to flesh out what you want to do in Greece/Italy/Spain -- my guess (just a guess) is you are trying to cram in too much there too.

Less is often more in travel to a certain extent. Plus traveling is costly too. Pair down up to half IMO.

Unless you are very lucky, it is unlikely that you will have so long to spend on a trip the long for quite some time. So I understand the temptation to cram it was full as possible, but I urge you to resist it.

one of the great things about modern day travel is that you don't have to make up your mind about where you are going to go too far in advance. ok, if you are wanting to stay in London or Paris at a reasonable price you should prebook, but otherwise, Trip advisor or Booking.com can be a real help in allowing you to book just a day or two before you want to move.

so perhaps start with a week in London and one in Paris and see how you feel then. you might find that you really don't want to leave.

If you want flexible travel however then vs full fare get some kind of Eurailpass - if booking discounted tickets then they are train-specific and usually cannot be changed and often not refunded. But serendipity is cool - on my first trip centuries ago I met folks to travel with and constantly changed course.

I agree with what everyone has said above. I totally totally understand the feeling of wanting to be able to see everything especially when you have no idea when you'd have that much time in the future to travel, but I think at a certain point the moving of hotels/flights, and in general just trying to get your bearings in a new place would end up making this feel like work, not a vacation. If you do actually have 60 days to travel and you absolutely want to hit all those places, the eurorail may be a great idea for that! I haven't been to all those places but Italy and Greece could easily be two weeks each and you'd still want to stay longer!

and using overnight trains can make getting between far removed places easy - like going from Munich to Rome or Venice to Paris, etc.