9 days. Start in Barcelona for 3 days, then to Valencia for business.....2 nights/3 days. Have 3 days to fill...fly home from Barcelona. Would appreciate suggestions between Valencia and Barcelona where 4 adults could relax and enjoy the sights. We do not want to spend all,of our time driving. Thank you.
Since you have to return to Barcelona, I'd just spend the rest of the time there. There is plenty to fill 6 days, and day trips to Figueres/Girona and Tarragona for a start.
Allow time to enjoy Valencia too. There are a number of worthy sights.
Have a look at my answer here: https://community.ricksteves.com/travel-forum/spain/spain-trip-september-2017