We stayed at the Hotel Jazz and loved it. I booked a triple corner suite and it was great. The couch would easily accommodate 2 kids. I think they let you put 4 in the room. It has an amazing rooftop pool and a great location. I think i paid 145.00 euros. If you can, try to spend more than one night in Barcelona. It was my favorite city on the cruise.
Glad to hear a review on the Hotel Jazz - it's on my "short list" for next summer!! It is one of the few that offer "triples". The pics online look like the room would have plenty of space! It gets great ratings on Trip Advisor too (#9 last time I looked). It also won the Trip Advisor 2010 Travelers Choice Award.
There are about 560 hotels in Barcelona that are reviewed on Trip Advisor - I am trying to stay within the top 200!! Other affordable family friendly properties on my "short list" which have decent ratings on Trip Advisor and which are also recommended in some of my tour books include:
Hotel EuroPark (#11 on Trip Advisor)
Hotel Barcelona Catedral (#17 on Trip Advisor)
Hotel Novotel Barcelona (#145 on Trip Advisor) (Novotel is a chain)
Praktik Rambla (#10 on Trip Advisor)
(have to book a "superior" room for an extra 30 Euro to fit more than 2 people)
Hotel Constanza (#34 on Trip Advisor)
I think Praktik Rambla & Hotel Constanza are more toward the bottom of my list only because they don't have pools while the others all do (big plus for kiddos). A couple of families on my cruise thread seem like they may book the Novotel - It just opened this spring & I've read the staff seems confused - but it's cheap & includes kids under 16 and you can include breakfast if you want. We're planning on spending a few nights in Paris pre-cruise & then will go to Barcelona the day before (to hopefully avoid any lost luggage). I may book the Novotel for the one night pre-cruise and then the Hotel Jazz for 2 or 3 nights after the cruise. I think I want to try 2 different places and I think the Hotel Jazz is supposed to be in a good location too.
A lot of the other properties just don't accommodate families or else they're really expensive by the time you price them for more than 2 people (some, like the Majestic charge extra for more than 2 people).
OOOPS!! I just reread the OP's post - she is looking for a property AT THE PORT to see the ship. I am not sure there's anything much available AT THE PORT that's affordable AND family friendly. Is the Diagonal Zero near the port? I know it's near Diagonal Mar Beach. Eurostars Grand Marina & the Hilton Diagonal Mar are near the port but not sure I'd categorize them as affordable.