Barcelona has much fewer 'must see' sights than either Paris or Rome do - Sagrada Familia the Gaudi Church, the Cathedral and old town area around it - the Park Guell - another Gaudi creation - the 'mountain' and its museums and attractions and IMO Montserrat is a highly recommended day trip.

But 3 days in Barcelona lets you see all the must sights - in Paris and Rome you have to categorize by your interests as there are too too many - like is Versailles a must sight in Paris - to me it is but it takes at least a half-dy getting there, touring around and back - but things you've heard of all your life and want to see put them first - you can always return to get more off the beaten path.

I would get a guidebook or two (you don't have to buy one or take it on the trip just get some from the library) and read up on the cities.

Why I say this is because everyone's interests and style of planning are different. I don't care for museums myself so that's the last place I'd want to spend time if I were in Paris.

I never plan trips, rather just arrive, get a street map, and start exploring. I plan each day the night before after dinner in my hotel room. And even that "plan" just means picking out a couple things to try to see or do. I like sitting in sidewalk cafes drinking wine, wander thru public parks and gardens, going to neighborhood street markets. Obviously others would think that was a waste to be in Paris and not go to the Louvre or whatever.

Make your trip your own!! Doesn't really matter what people here think or do.

My method doesn't work is you simply MUST see something or you will have regrets.

And I do believe she's still going to all 3 cities in only 10 days, so there's simply not a lot of time to plan (after you subtract the time going place to place).

Had spend a night / 2 days in Barcelona after a cruise back in Oct 2007
Stayed at Citadines on La Ramblas (friend stayed & recommended it)
Love the ideal location, within walking distance to metro, shopping, eating &
Sightseeing
Planning to go back again in Oct 2014 as price for location -excellent value
Read it was renovated in 2013
Expedia has best rate

suze--While I strongly agree that you should "make the trip your own" despite what others think, my experience has been that this takes even more forethought and planning than simply ticking off the "top five" or whatever sites in each city.

Spend your days mostly in the streets and hanging out in cafes and tapas bars. That will take the stress out.

Sounds like you're gonna have 3 at each regardless of well-intentioned advice above I shall not repeat, so here goes:

Rome:
Colosseum
Forum
Pantheon
Piazza Navonna
St. Peters & Vatican
Trevi Fountain

Paris:
Arc de Triomphe (via Champs E thru Tuileries)
Orangerie
Notre Dame (then behind to)
Ile St. Louis (then across Pont Neuf to)
Luxembourg Gardens (thru St. Germain)
Rodin Museum & Invalides
Pont Alexandre bridge back over to rt bank
Montmartres/Sacre Coeur
Place de Voges


Barcelona:
Ramblas
Sagrada Familia
Casa Batllo (liked much more than La Pedrera)
Mont Juic & Miro Museum
Picasso Museum & Gothic Qtr

These came foremost in my mind as tops for must-see, and we did the Barcelona & Rome sights listed above in 2-3 days, returning to Rome some years later. If weather is bad in Paris then perhaps you can venture into Louvre, but think strolling outdoors to points above captures more of the City, taking in right & left banks. Go for it!