Our family of 3 (includes teen son) are spending 4 nights in Barcelona and 4 nights in Madrid in the month of March.
What areas/barrios should I look for lodging on each city? Looking for safety, convenience to sights/transportation, comfort, character and a good night of sleep (not too noisy if possible).
Hotel (suggestions?) or short term rental? If STR, I usually use Airbnb in the USA, would that be the way to go, or is there a better site for Spain? Thanks in advance!

As mentioned , knowing your budget may help with suggestions.
Some years ago, we rented from Habitat Apartments in Barcelona,
Home Club in Madrid. Both good .
Booking.com also lists apartments on their site.

The first time visitors often stay in Barrio de Las Letras in Madrid and close to Plaça de Catalunya in Barcelona,

[QUOTE=danon;17628319]As mentioned , knowing your budget may help with suggestions.

$150-300 per night

[QUOTE=crazyfornps;17628520]
If you search booking.com you may get some ideas .
For the good location I think you will be looking at the higher end of your budget ..
If you find AirB&B you like , you can get information about the location here.

Thank you for the suggestions!

Eixample is a good area - quieter but not far from things you’ll want to see and do. Many good restaurants in that area too.

The Mercure Madrid Centro is a really nice hotel that is within walking distance to the Prado, Reina Sofia, and Retiro Park. Can also walk to other places. Lots of restaurants nearby.

The Eixample neighborhood in Barcelona is a wonderful neighborhood to stay in. Beautiful architecture and very centrally located.

It's been a few years, but we stayed at the Hotel Jazz in Barcelon in the Eixample neighborhood. Great location and hotel was relatively new when we stayed there, maybe 15 years ago

IN Barcelona, I like the Eixemple area and the area around placa de Catalunya (not right on it). I've also stayed in Hotel Jazz once and liked it ( I think technically, it's right on the border of the Eixample and Ciutat Vella districsts but it's only a couple blocks from place Catalunya and not what people usually are talking about when they say to stay in Eixample, but something farther up). There are other areas some tourists like that are farther out (Gothic isn't farther out but may not be as convenient for public transit).

I've stayed in the NH Gran HOtel Calderon also and loved that location The NH is a good Spanish hotel brand, I think.

Really, it's like almost any European city, first time tourists usually want to stay in the old town center area.
In Madrid, I like the area in between Gran Via and Plaza Mayor, but Lertras and the area near the Prado are nice, also. My favorite hotel is the Palacio San Martin which is a very convenient location but off the main streets to not that noisy. this is it
https://www.intelier.com/hotel-intel...martin-madrid/

Thanks everyone for your wonderful suggestions and the explanations that went with! I have chosen apartment hotels, on Passeig de Gracia, 64, Barcelona, and Grand Via 14, Madrid. If you have any opinions on these locations or suggestions, please let me know

very central, very busy avenues.
try to get rooms in the back