Tony at www.calidafishing.com will do leisure trips as well as a fun day fishing. They are based in the first small marina at Puerto Mazarron.
We have also used www.chartermuffy.com based on Mar Menor.
This year we enjoyed a half day with www.go-n-sail.com but they are seasonal at Puerto Mazarron (only there July/August. Based at the Mar Menor the rest of the year, I think.
All recommended, some more luxury than others but all good!