I don;t think she's a heavy spender - I couldn't begin to do it for that. But I'm not 19, staying in

I will be studying in Leeds, the UK from september to january and have one month christmas break from December 7th - January 6th. My boyfriend will meet me in London, and from there our trip itinerary is as follows:
We have already booked our accommodation in London and Barcelona, and our flights to Barcelona small cruise ships to alaska and Paris, but beyond that we are flexible - ideally I do want to spend Christmas in Vienna and New Year's small cruise ships to alaska in Berlin but I am wondering whether we should have an extra day in Paris or in Rome.
We are travelling small cruise ships to alaska on a reasonably moderate student budget (around 4000 euro) and would prefer to wander around cities and see architecture and get a feel for the atmosphere rather than spend all our time in museums (with some exceptions maybe), despite the expected cold weather. I will be doing some shopping but probably will focus on second hand or less expensively priced boutiques rather than just big designer stores.
Does this trip sound achievable? Is there anything I need to consider? Where would a fifth night best be spent? (Paris vs Rome, or should we attempt an overnight small cruise ships to alaska trip to another French or Italian city/town with the extra day?)
fly fly fly - you will only see heavily touristed tourist meccas and nary a wee bit of the lay of the land that lies between the big cities - tarmac and big cities but not say Switzerland as you might pass thru on the train.
Strongly consider IMO bargain Eurail Youthpass, if under 26 that is, and avail yourself of the way to not only see the often wondrous countryside between the tourist meccas and also meet and mingle with Europeans, who often take the train as well as zillions of young folk from around Europe and the world riding European trains.
Anyway srongly consider a major re whatever of your trip and take to the rails - great sites IMO for learning and planning a European rail adventure - www.budgeteuropetravel.com , www.ricksteves.com and www.seat61.com .
I so agree with Pal. Taking the train accomplishes two things: You get from point A to point B and, unlike small cruise ships to alaska the plane, you save the cost of a hotel each time you train overnight. And, you are city center to city center, saving you the cost of a taxi, train or shuttle to and from the airports.
If it were my trip, I'd pick destinations that are not quite so geographically separated and are, where possible, reachable by train. You've also picked only big cities. I'd want to mix it up a little with a couple of smaller, quieter destinations.
You need to note what days of the week you'll be where and what things will be open. For example, if your only days in a city are Sunday-Monday, you might have trouble seeing everything on your list.
Granted you are going off-season - but that doesn;t make things small cruise ships to alaska free. I woulld do some searching small cruise ships to alaska now for lodging costs - and organize your flight plan to you are ready to pounce the second you get get a super bargain fare. (My 19 year old daughter went to europe with 2 friends last summer for 5 weeks - modestly, no shopping and limited student price nightlife - and she spent more than $8000 for one person - including trains and intrercity flights - but not the transatlantic flight.)
She's a heavy spender. Not counting international flights, my wife estimates an expenditure of $5500 for two months for the two of us (she thinks that this is actually high). Admittedly 4 weeks were rent "free" (the costs are hidden in annual taxes, telephone bills, utility small cruise ships to alaska costs, house repairs etc.), but it includes flights from Poland to France and three different car rentals for a total of 48 days.
I understand you are not afraid of cold, but Amsterdam is wet too. You really can't walk around small cruise ships to alaska in the rain all day in December. Have back up plans for indoor activities that will genuinely interest you and your boyfriend.
Traveling out to all those departure airports, arriving about 2 hours early each time, traveling in from all the arrival airports -- you are spending easily 8 or 9 days of your month just in transit. That is a huge waste of time/money.
I don;t think she's a heavy spender - I couldn't begin to do it for that. But I'm not 19, staying in a small triple and don't want the type of hotels or restaurants/cafes they used - and definitely don't want low budget airlines or trains (except if just between two major cities).
We like to do one splurge restaurant in each city and stay in a central full-service hotel with enough room to relax (usually a small suite). IMHO at a certain point in life comfort is more important than $.
What does the 4,000 include? Does this amount include transportation and and hotels? I would cut back to about four destinations and try to travel by train as much as possible. If you stay a week in each place, you could find a small apartment which would be much cheaper than hotels. If course, if you're small cruise ships to alaska planning on staying in hostels that can be inexpensive as well. Three days is not nearly enough for Paris.