The Lucca old city is fabulous to visit and to relax. The best activity is to walk or cycle all the way around the top of old city walls stopping on the way for a picnic and to take pictures.
One could consider to stay outside the old city which would be less expensive and just walk in daily. A must do is to take a train from Lucca to the 5 fishing villages of Cinque Terre.
Lucca is really nice. Just eat at trattoria da Leo and everything will be ok haha. No but really there's enough to see.
Just stay for a mx of 2 nights. We only stayed like 1 night and it was enough, but we really enjoyed it for the time being.