suggestions - 8 days in Spain starting from Barcelona

Girona is a town worth considering, with access to and from Barcelona. Were you thinking of 4 days for Barcelona and 4 for Madrid? If you did 3 apiece, that would leave 2 days (nights?) for another northern Spain location, in the Basque country. Maybe San Sebastián (also known locally as Donostia) or Bilbao. The old town in either is a special place to stay.

I will be in Spain for 9 nights.

Sitges.
23 minutes south of Barcelona on the R2 sud
We loved the town/city.

I would do 5 days Barcelona and 3 days Zaragoza.
We really enjoyed Zaragoza.

A tricky situation, August is the height of the tourist season in Barcelona, one of the most visited cities on the Earth. It's going to be absolutely packed.

You can try to commute in from a nearby town or city, but honestly I'm not sure if it's practical going so far as Girona or Sitges. You may want to look at San Cugat as a closer option. I think you may just have to bite the bullet and pay the extra cost to stay in Barcelona as you'll have to compete with thousands of other peoples to see the top sites.

Or you could just skip Barcelona and maybe spend a few nights in Valencia a few nights in Madrid and a few nights in Zaragoza. Before flying out from Barcelona. Wherever you go it's going to be hot as hell too so be prepared for that.

Ditch the hotels and book an apartment for the benefit of family enjoyment. Barcelona offers a HUGE menu of opportunities and a wonderful well connected transport system. Example: you can catch a subway to connect to a train creating a seamless full day trip to Montserrat
https://www.barcelona-tourist-guide.com/en/tour/montserrat-spain.html
We often stay in the Diagonal Mar area
https://www.google.com/maps/place/Barcelona,+Spain/@41.4070433,2.2127491,15.07z/data=!4m6!3m5!1s0x12a49816718e30e5:0x44b0fb3d4f47660a!8m2!3d41.3873974!4d2.168568!16zL20vMDFmNjI?entry=ttu
This area takes us out of main stream tourist zone while offering ez connection to all points Barcelona and surrounding areas. The non-tourist beach areas are at your fingertips plus a nice mall for all to enjoy and local restaurants with great experiences at better prices.
Suggest two alternatives:
A) spend the entire stay at one location in Barcelona and take deep dives into huge variety of day trips. I know, sounds crazy, but this choice does offer a wide variety of experiences without needing to change locations. There is a lot to be gained without needing to move a platoon/family from one point to another. Imagine the benefit of unpacking once in an apartment where you can start with making your own breakfast and save money on snacks by having a refrigerator for the family.
B) Five days in Barcelona and Three days in Madrid, will use apartments
Big tip...................hats for everyone and stay HYDRATED. Do everything possible to not bake your heat in the intense heat.

Castelldefels is a beachfront suburban town that’s only 12 miles from Barcelona and just a 27-minute ride from the Passeig de Gracia train/Metro station in central Barcelona on the commuter rail line called “Rodalies” Direct buses depart from Terminal 1 at Barcelona’s airport and reach Castelldefels in 25 minutes. There are several hotels available now in the $150-$225 range for late August. Sitges, while charming, is more of a resort town with generally higher hotel prices. It’s also a minimum of 41 minutes to reach Sitges on the Rodalies commuter trains, which makes it tough to return to Barcelona if your group needs to rest in the heat of the afternoon. And—as Carlos says—it will be HOT in August with high temps averaging F 85’ in high humidity; lows average 74’ I made reservations four months ago for early September in Barcelona and the rates have more than doubled since then.