The zoo is a little old and cramped - it is a city zoo - but big enough for a day/long afternoon's walk around (you can take your own food in, there are picnic tables and drinking fountains dotted about. There is also a twice-daily dolphin show. Don't let the queue put you off, there's always plenty of room.
Overlooking Barcelona is Tibidabo, an old-fashioned-looking funpark with fabulous views. Also a tram/funicular to get you up there.
The cable car from Montjuic to the beach is great if you and dc don't mind heights. On Montjuic there is: Miro museum, Olympic bits, bottanical gardens. At the bottim of Montjuic in Placa Espanya are the Magic Fountains: watch the 'Barcelonaaaaaa' Freddie Mercury video and you'll see dancing fountains with lights andusic. Cheesey, free fun! Oh, and there are loads of parks around Monjuic that have things you can bounce on/hit/speak into etc to make noise! If you don't get up there, then the best park is right next to the zoo: Ciutadella.
There's a chocolate museum in the Born, plus a converted market (huge) that you can access freely, with old Roman bits in. It's recently opened. You can see the old Roman road that went through rhe city. There's a small Egyptian museum on Valencia syrett, just off Paseo.de Gracia (main street, very close to city centre).
Pigeons in Pl Catalunya. (Ok, not everyone's cup.of tea!) . The El Corte Ingles there is a huge department store - with loos! Barcelona lacks public loos, so unless you go to a cafe and buy a bottle of water or sneak into McDonalds for a McWee that's your cleanest bet!
Public transport is great, metros clean and efficient and just below street level. Or the tpur bus/es are great, they go everywhere - including Camp Nou, if your dc like football.
Easter will be lovely and warm (curently 17c) and May will be getting hot, around 23-25 not unheard of.
If you do head to the beach, aim for Vila Olimpica (there is a metro stop) rather than Barceloneta as it's a shithole (sorry!). Fake sand, ie dust, and it's dirty.
Fabulous city, enjoy!