Honestly, Barranquilla wouldn't be my first choice. It's a noisy, messy city. If what you want is a coastal city, beaches and all, your best option is Cartagena, although be forewarned that housing costs rival Miami's. I prefer Santa Marta myself, which is less touristic and is very close to the incredible Tayrona national park. Other, more rustic options are Tolu and Coveņas, to the west of Cartagena. Wherever you settle down on the Caribbean, you'll roast! It's 5 shirt a day weather, year-round, and there's no relief at night! Water shortages are common, service cuts sometimes lasting weeks.
If you don't mind changing the sea for the mountains, there's lots of options in the interior, starting with Medellin. I could go on, but maybe you can just visit my blog for more answers.