In a word, YES! Girona is a welcoming, high-end city with plenty of tourist attractions to fill any tourist's dance card for a fun day outside of the hustle and bustle of Barcelona.
Getting to Girona from Barcelona for a day trip could not be easier. Spain's high-speed train system can get you from Girona to Barcelona in less than 40 minutes.
There are cabs waiting at the station, if you're not ready to start the walking quite yet, but it is a perfectly pleasant walk, with coffee shops, etc.
Founded in 79 B.C., this former site of a Roman citadel carries its age well, blending historic buildings with modern ones, without losing its historic flare.
Modern Girona is certainly not a large city, with a population of just over 100,000 as of 2019, but it really doesn't feel terribly small.
Absolutely. Girona is relatively small, and hugely pedestrian and tourist friendly. Once you're in the historic core, a car would be a massive burden.