Travelling by train from Florence to Pisa in April. Would like to spend one night in smaller town/village en route, conveniently located near train. Does anyone have recommendations for a one-night layover? I am interested in scenery, history and food.

It's only a 1 hour train ride (with no stops, as I recall). Why not stay in Pisa? There's a lot more to Pisa than a leaning tower. Take some time to explore the city, outside of the Campo dei Miracoli. Once you get away from that area, it's a decidedly untouristy town.

Grasshopper's right! There's more to Pisa that just the tower.
Lucca is also a very pretty city. It's only half an hour by train from Pisa but it's not en route to Florence.

definitely spend some time in Lucca.

To clarify, we are flying into Pisa Monday night and staying overnight. In the morning we plan to travel to Florence for two nights (Tuesday and Wednesday). We are wondering what to do on Thursday night, before we have to head back to Pisa to fly back to Paris. Any suggestions would be helpful.

Lucca definitely. Short train or even cab ride to Pisa (I don't think the cab was over $20US).
Lisa S