Nice overnight stopover on train route to St. Ives

Exeter would be a good place. It has most of the old city features, walls, old buildings. Except for one part that got destroyed in WW2 and rebuilt.
Plymouth is not a tourist city, completely destroyed in WW2 and re-built on a completely new street plan.
Liskeard is good for one night, and also Truro.

A tip: do not fly into London Heathrow, London Gatwick is better if you are catching a train to Cornwall. It has more flights from Barcelona, but the real reason is there is an hourly train from Gatwick to Reading, and Reading is the first stop outside London for the trains to Cornwall. So you avoid going into London.

Thanks, Chris. I had not considered Gatwick, but we will be flying BA and they have frequent flights into LGW as well. So we can do that.

I am also wondering if we should just do the night train, which I believe means starting at Paddington just before midnight. I will have to see which my husband prefers.

You could have saved time and hassle by flying direct from Barcelona to Bristol - which has frequent trains down to Cornwall.https://www.skyscanner.net/transport/flights/bcn/bris?adults=1&children=0&adultsv2=1&childrenv2=&infants=0&cabinclass=economy&rtn=1&preferdirects=true&outboundaltsenabled=false&inboundaltsenabled=false&oym=1806&iym=1806&qp_prevProvider=ins_browse&qp_prevCurrency=GBP&priceSourceId=b3ms-NL1-1&qp_prevPrice=101&selectedoday=01&selectediday=01

For a place to stop near the water, you could have a look at the Torbay area (Torquay, Paignton, Brixham). It's only a short side trip off the main train line, by train or bus from Newton Abbot. Bus service in the region is excellent.

It's a major English seaside destination, so it's a touristy area, but few Americans go there, so it still has a little bit of an off-the-beaten-path feel.

The South West Coast Path on the peninsula east of Torquay has some very good scenery.