Which area of Barcelona to stay in with family

Catalunya is a transport hub that will get you to and from Barcelona’s sights without much hassle. Good areas to sleep near Catalunya are the Barri Gotic (Gothic Quarter) located southeast of Catalunya and Raval located on the southwest side.
Some posts say this is a seedy area but I stayed north which was quite nice. I believe it's when you go further south is when it changes.

The Raval area has a somewhat rougher feel to it than other parts of the city near Placa de Catalunya. It isn't an area I'd recommend staying in for those who are not seriously pinching pennies. I (65-year-old female) didn't feel uncomfortable there in the daytime, but I did think to myself that some folks definitely would be, and I didn't walk through the area at night. It's important to remember that dinner is very late in Spain, so one can easily be walking back to one's hotel after 11 PM (though there will be others out and about, too).

There have been reports within the last two or three years of an uptick in street crime in the Barri Gotic, including some strong-arm robberies. It's definitely a picturesque area I'd recommend every tourist see, and I haven't heard that it's uncomfortable-feeling, but it sounds as if it's not the best place for a family to stay these days.

I trust we'll hear from at least one of our Barcelona residents soon.

It was a while ago but we were very happy with our stay at the Hotel Continental Barcelona. It was reasonably priced..our foremost criterion. It is located on Las Ramblas, about a one minute walk to Plaça de Catalunya so ultra convenient to transportation connections and all the sights and activities of the street. They offered a buffet during the day including food and drinks which may be a big selling point with three boys. There was nothing posh about this hotel but everything was great and the staff were very helpful. Apropos another recent posting about Rick Steves discounts…I never asked but the clerk who saw me passing through the lobby one day with my RS book under my arm stopped me to tell me I was entitled to a discount which he applied to our bill. Majorly fond memory. Safe travels.

You might also consider the Eixample area, northeast of Placa Catalunya, with wider streets, lots of interesting architecture, and very walkable. I haven't stayed there but I expect it would be pleasanter at night. I stayed at the Hotel Catalonia Portal de l'Angel, on a pedestrian street between Placa Catalunya and the Bari Gotic, and it was fine. When I visited (October 2019) there were nightly mass demonstrations supporting Catalonian independence, with heavy police presence and a lot of overnight graffiti. I kept my distance and didn't feel unsafe, but the sights and sounds were unavoidable. That makes my experience of Barcelona "nightlife" atypical.

I would also not recommend staying in El Raval, it's a seedy place known for narco-trafficking and prostitution, I don't want to scare you too much, but there has recently been a spike in violent crime in that area, especially at night.

I instead would recommend you look at the Gràcia district, specifically the Vila de Gràcia neighborhood. It feels very cozy and welcoming, with many young families out and about. Gràcia used be its own town, before being incorporated into Barcelona in the late 19th century, so it still retains its own small town feel and charm. For food in the area, there are many great Italian restaurants, gelato, and Pizza shops here, due immigration here by young Italian families.

I would also not recommend staying in El Raval, it's a seedy place known for narco-trafficking and prostitution

I stayed in this area in 2008 and loved it and had no idea it was a bad area. However, I stayed north quite close to Catalunya at a Rick Steves recommended hotel.

@MaryPat that area in general has gone down the drain since 2008 (14 years ago), especially the last decade, mass tourism and other socio economic issues have deteriorated few other areas of the city, Sant Pere is another part of town I'd avoid after dark.

I recommend staying in Eixample. It's a beautiful neighborhood and very convenient to many sites. We felt very safe there. We stayed at the Gran Via Hotel. We also enjoyed walking around Gracia and having lunch there, so that would be a nice place to stay as well.

First, consider renting an apartment. Doing so gains more space with a kitchen, family room and separate bedrooms. You definitely can find apartments under your budget of $500 a night. Highly recommend staying within the Eixample which is safe, entertaining and offers easy access to a wide range of experiences.

that area in general has gone down the drain since 2008

I was in Barcelona again in 2018 and walked through El Raval during the day and did not notice anything unusual. Of course I was further north too.