Since I have not received much feedback, I am reposting my itinerary in a new message, hoping it will be noticed, and maybe more people will be willing to advise/comment.
Please, share your thoughts.
Thanks for your time and input.
Agnes
HERE it IS:

Barcelona ITINERARY (6 nights) - Wed 18th - Tuesday 24th July, 2007

Day 1 Wednesday
Our flight arrives at 14:35 (or 2:35 pm)
Wednesday Evening
Barcelona Cathedral
Barri Gothic

Day 2 Thursday
Sagrada Familia in the morning
Eixample – a stroll down Passeig de Gracia
(Casa Battlo) - interior
Lunch
La Rambla Walk (Boqueria, Esribe)
/Teatre de Liceu, Placa Reial/

Barceloneta in the evening (or, should we do Barceloneta Wednesday evening after we arrive, and Cathedral and Barri Gothic Thursday evening ???)
Does it seem feasible?

Day 3 Friday
7:50 am flight to Seville, arrival in Seville at 9:25 am
Cathedral/Giralda
Alcazar/A. Gardens
Flamcenco show (Can you suggest a place???)

Staying overnight (Hotel Dona Maria)

Day 4 Saturday
Seville
Barrio Santa Cruz
Flying back to Barcelona at 16:30 (4:30 pm), arriving at 18:00 or 6 pm

Day 5 Sunday
Museu Picasso
Beach and/or Monjuic in the evening – just for the view

Day 6 Monday
Monserrat ¾ day
Beach in the evening

Day 7 Tuesday - Leave

Thank you!
Agnes

On Thursday, you are planning to have lunch and then go to the Boqueria. I would suggest having lunch at one of the stands inside the Boqueria market building. I have been to Pinotxo, run by a colorful character, and to the Kiosk Universal. Both great for fresh food from the market.

On Sunday, you could go to Barceloneta after the Picasso Museum and have a seaside lunch there. Then you could take the cable car to Montjuic. Check the cable car hours; when we were there in February they closed down in the middle of the day for lunch, and I don't know how late they operate.

Dear Agnes:

I think you should skip Seville and concentrate on the area around and nearer to Barcelona. Go up to Girona/Fiqueres/Costa Brava. We visited Cadeques for 3 nights last summer and enjoyed it very much.

Save Seville and S. Spain for another trip.

MY

Everybody - thank you!
I will rethink my itinerary!
Agnes

Hi Agnes, I agree with the idea of saving Seville for your next trip... We are in Barcelona right now and we enjoyed Park Guell and La Pedrera very much too and I didn't see those on your itinerary. We took the cable car from Monjuic across the harbor to the beach and it was great. But the cable cars going up to the Military Museum on top of the hill are not operating yet so if you want to go up to the castle, you need to hike a bit or take a bus. We found a place called Tapa Tapa on Passeig de Gracia right across from Casa Batllo serving very good tapas with pictures of all the dishes (more than 50 different kinds) so making ordering very easy especially for us knowing no Spanish. We are enjoying our last couple days in Barcelona here and I am sure you will like the city as much as we do. Have fun!!

bookmarking

I am going this week and my itinerary is pretty packed compared to yours, so I'm sure you will have a relaxed trip, unless, of course, you want to do much, much more.

Dear friends are in Barcelona now and we are arriving in May.
They are raving about the free, downloadable "Maribel's Guide to Barcelona".
M

Yes, absolutely take a look at Maribel's guide, which is available at www.maribelsguides.com.

Everybody, thank you.
Believe it or not, Spain is not tangible to me...I am trying to say it is abstract.Even though I have read 2 guides and watched a program on Barcelona on Travel Channel, I still do not know what to expect...
This curiosity was the reason why we picked Barcelona over Florence...
So, I am trying to make my trip exciting, yet at least somewhat relaxing.
I will try and rethink my itinerary.
I will add some things to it
However, I think Seville (flying and staying overnight) is a keeper.I am not trying to kill myself and seeing everything there is to see in Seville in 24 hrs. I just want to see the Cathedral and Alcazar, and Santa Cruz disctrict...maybe a flamenco show.
I can always come back to Spain - if it captures our hearts (so far, Italy is the winner)
I will modify my itinerary a bit - I tried not to overload it - this is what I usually do. You should have seen my tentative Florence itinerary
Thank you very much.
Any more feedback is welcome and much appreciated.
Agnes

I am going to Sevilla and Barcelona in June (along with other stops in Spain including Madrid and Granada). The two Flamenco shows recommended on another forum were:
Casa de la Memoria de Al-Andalus and
Los Gallos http://www.tablaolosgallos.com/

The discussion on Flamenco my have been on tripadvisor -- can't remember.

Robin

Mikemo & Nikki,
Maribel's guide is great!
THANK YOU.
Mriscuit, what does YOUR itinerary look like, if I may ask?
Robin - thanks for tips on Flamenco shows.
Everybody else. THANK You.
And more feedback still appreciated.
Agnes

Have you thought of taking the train down to Sitges for a day. It is only 20 miles or so.

I will research the town of Sitges.
It might be a nice idea to go there, walk around, and go to the beach.

Thank you,
Agnes