Barcelona accommodation in safe neighborhood near Placa Catalunya

Barcelona is a city where short-term vacation rentals have become a problem for the local residents, so I would suggest booking an Aparthotel rather than AirBnB.

Apartments Sixtyfour in the Eixemple, a few blocks from Plaça Catalunya, looks like a good choice. We have not stayed there, as we have chosen hotels instead for Barcelona, but it gets very good reviews. They get a 9.1 “wonderful” rating on booking.com (but you should book direct).

https://www.sixtyfourapartments.com/en/

I would be challenged to name an "unsafe" neighborhood in Barcelona.
You can stay in a perceived "safe" neighborhood and still be pickpocketed IF you choose to not take recommended precautions. My point is to focus on the common sense precautions regardless of where you stay. Barcelona is our favorite most often visited destination where, over the past four decades, we have witnessed the impacts of tourism volume and velocity. Yet, we have never felt threaten during any oof our journeys.
An ounce of prevention.................

I would be challenged to name an "unsafe" neighborhood in Barcelona.

They exist... Raval, La Mina, Sant Pere to name a few

I've had no problem whatsoever with street crime in Barcelona, but it should be noted that the Raval and Sant Pere areas are parts of the city where tourists could easily find themselves. I walked through the Raval a couple of times back in 2016 and was aware it would be a somewhat uncomfortable area for a lot of US tourists--primarily those who don't live in urban areas and move around on foot a lot.

Love the Ravel and enjoy the diversity and grit. The Mercat de Sant Antoni is a favorite place to shop for vittles and restaurant prices are so much cheaper. Via walking we have found where several artists have small storefronts where they create goods often sold in the main tourist zone. Bunches of students who we have followed to "rustic" tapas bars. Tis one of the few areas remaining untouched by the growth and velocity of main Barcelona tourism.

I have stayed at two of the hotels in the H10 chain near Placa Catalunya and can recommend them. We enjoyed the H10 Metropolitan and the H10 Uriquino Plaza. Join their H10 Club and you will get a free breakfast and a discount. We felt safe in Barceona and enjoyed this area since it allowed us to get to many sites. Taxis are very good in Barcelona so if you feel unsafe, then just take a taxi.

We also stayed at the H10 Urquinaona(sp)?. We upgraded to a balcony room and I can say the service and hotel were wonderful. It's walkable to a lot of places and outside is a metro station.

In April, I stayed at the Hotel Reding Croma in the Eixample neighborhood. Safe area, clean and modern furnishings, walking distance to Placa Catalunya, Urgell metro station and the Block of Discord. Lots of restaurants nearby and around the corner from an Aldi.

I am also going to be in Barcelona, in July, and looking at staying near Placa Catalunya. Sounds like that particular area is fairly safe, relatively quiet? There are a couple of H10 hotels I'm looking at or Catalonia Square hotel. Is this area considered Gothic Quarter? Looks like right on the edge between GQ and Eixample.

Should we consider an AirBnb or is it not a good idea for Barcelona? We're a family of 3, and although the AirBnbs don't seem to be any cheaper than hotel rooms in Barcelona, they would give us more comfortable space. I'm just not sure how trustworthy they are given all that you hear about scams.

Only four nights isn’t long enough to bother with an apartment and what it entails.
We spent a week at a wonderful aparthotel, Hispanos7Suizas, near La Sagrada Familia. It had all the amenities you need.
As far as street crime, we were warned about it every time we left our apt building and in restaurants. Be very aware, hold on tight to your possessions. We were constantly warned about this in restaurants and by our aparthotel’s concierge