My husband and I will be visiting the following places for one day each on our transatlantic cruise from the states to Barcelona: Azores Portugal (12pm to 7pm), Malaga Spain (7am - 8pm), and Cartagena Spain (7am - 2pm). What would you recommend for our very short time at these stops? I read a rec to take an open topped bus tour on Malaga. Other than that, not much else. We're on a tight budget but would love to experience as much as we can within the few hours we have. Oh, food recommendations would be greatly appreciated as well. Bring on the Tapas.

I don't know if this matters but we will be visiting these places at the end of April.

Can only help w/Barcelona:

Park Guell (Parc Guell) with Antoni Gaudi works is free
and his Sagrada Familia church which is still being built
Fee for inside entrance

In the Azores, in Lajes, I had a fish dish that was absolutely superb. I'm sorry, I don't remember the name, but I was told that it is a specialty of the Azores, so you should be able to get it most anyplace. The restaurant offered two or three choices of type of fish, like Rock fish, Flounder, etc., but the preparation was with potatoes and a cheese sauce. I know it sounds odd, but it was one of the most memorable meals I've ever had.

I think you will want to rent a car or hire a driver for most of your time there.

if you are on a tight budget then forget tapas....Menu del Dia is always much better value for money. Lager portions too.
In the times given you have to allow an hour or so to embark/disembark too

About Malaga, I can recommend you to spend the day in the city. Read in this forum a lot of advice I have posted.