The ruins of Empúries are not near Castelló d'Empúries. You should go to another town called L'Escala. The obvious option to get there is by car. If you opt for public transportation, you have direct buses from Barcelona, but I doubt that they take less than two hours. Even breaking the trip in Girona or Figueres would not save much time, if any. However, as Belsaita stated, it would make sense to spend one or two days in one of those of towns, which are two major destinations in Catalonia, the first for its beautiful old town, and the latter for the Dali Museum. The ruins are outside of the town center, near the village of Sant Martí d'Empúries, but whether the distance is walkable, will depend on you. A taxi ride from Girona to the ruins, according to worldtaximeter.com would be around € 60,-. If you are three of four travelers, that should be quite reasonable.
I hope you enjoy your trip
We hired bikes from Nou Emporda bikes (on the main Av. de Gerona about 5 minutes walk from the central tourist office). The service was friendly and helpful, helmets were available, and the bikes were in good condition. http://bit.ly/iLck0c
I'm really glad we rented bikes. This area is very flat, and the surrounding countryside is beautiful (in early June all the fruit and cereals are still to be harvested). There's a well-signposted circular cycle route from L'Escala to St Pere Pescador, St Marti etc. going through several lovely hamlets and villages. It's about 25 Km and you can do it easily in half a day. If that's too much for you it's easy to cut short - just look out for the green signs. Most of the route is on farm tracks (no tarmac) so I would recommend a mountain bike. We went on a Monday, and encountered no traffic except a tractor!
Here's some detail on the route: http://bit.ly/kmxNqR
Are you nervous about taking your baby or child on a plane trip? You aren't alone, most parents are nervous about it. We have moved with Iris and Sam Tarragona Corfu by plane this holiday and drove some distances by car on the island itself and we learned a few things that hopefully will help you.
Bring books, old favorite toys and new surprise toys. Do remember that balls are not a good idea as they can end up anywhere! Our best buys were definitely books, especially sticker books are great! They can peel the stickers off, are glossy, have thick pages to turn easy, have bright colours and come in endless subjects. They're a nice break from the other books your child might be tired of, too. Put aside fears of setting poor eating habits, and bring on the snacks! We told Iris: “Welcome to the world of boredom eating."
If your child is big ask for earplugs as soon as you board the aircraft. Make use of them for take-off then save them for landing as the crew may not have any fresh ones left by then. Also let them eat candies, this helps the kids tremendously if they don't know how to pop their ears.
Toy bars meant for stroller use are a big help in the car, as they often feature toys plus a snack cup, and are big and easy for you to grab from the front seat for refills. During the car trip it’s always a good idea to play a game and sing some songs. It sounds rather easy, but it does work!
We only have one last statement! Just do it! Don’t be afraid that it might go wrong. We have learned this, because we have been travelling with Iris from the beginning. She was only 6 weeks young when we had our first short vacation and stayed in a hotel. Iris has been used to it rather fast and (maybe because of it) has always been an easy kid to get along with.
If you don't have your own transport the best option is take the Sarfa coach.
You can take the bus at Estació del Nord (Barcelona)