This neighborhood is tough to describe geographically since it is shaped sort of like the head of a giraffe eating a flower. In any event, the neighborhood boundaries are Carrer de Rosselló to the southeast, Carrer de Sardenya to the northeast, Carrer de les Aigues to the northwest, and approximately the Avinguda de la Republica Argentina to the southeast. Generally speaking, it is a small, hilly neighborhood and more or less an upper-middle-class neighborhood. The famous Gaudi-designed Casa Vicens and Parc Güell are both located here, as are other landmarks.
The denser and busier area of this neighborhood is located between Travessera de Dalt and the Carrer de Rosselló at the southern corner. It is an area filled with commercial streets, apartment buildings, parks, and other green areas. One of my favorite corners of the neighborhood is the Plaça de la Virreina located near Calle Or. There is a church on one side, restaurants, and cafes on two sides of the square, and a large open area where you can hang out or have your kids run around. I personally recommend walking in this area. Additionally, just 10 minutes away on foot, you will find the first house Gaudi designed. It is an extremely interesting house, now a museum, with a café and a patio area where you can sit and eat. You can actually visit the café only without going into the museum.
The Passeig de Santo Joan originates in the eastern side of Gràcia and ends in the Barri Gotic. In Gràcia, this Passeig has a large median in the middle with mini playgrounds along the length of the road. There are also shops and restaurants on opposite sides of the median. Here, as well as all over the neighborhood, you can find places to live in several price ranges based on the amenities. Also, Gràcia has a good reputation in the city as far as districts go, which is well deserved. The district/neighborhood is typically well-maintained, safe and affords many options for things to do.
If you go farther afield, towards the northwest, you will reach the Parc de la Creueta del Coll. This is an immense open, green area that is great for hiking, picnicking, hanging out or cooling off in a large splash area. It is a bit off the beaten track, but it is worth it for the park experience, as well as the views you can behold from the summit. Since it is a little far, make sure to pack your own snacks and water, or else hike over to the local “chiringuito” (snack bar.)
For me, personally, the Grácia neighborhood is one of the best locations to live in Barcelona. It is centrally located, has good transit access to most of the city, and there are great eateries, small shops, and pedestrian walkways or alleys, which give the area the feeling of being a small town; especially around the Plaça de la Virreina. Additionally, the Parc Güell is going to be a go-to place with friends visiting from your home country. It is a hike getting up there from the Plaça, but it is doable and you can stop and take as many breaks as you want at the many cafes along the way.
When planning where you might want to live, check and see if living close to highway B-20 will help your commute. This open roadway provides quick access by car to the airport, outlying suburbs, and the other northern districts, such as Sarriá, Horta-Guinardó and Nou Barris. Also, as a parent, you can live in northwestern Gràcia and take the highway to Pedralbes, should you place your kids in a school in that neighborhood. Read more about Les Corts.