Nantes being a great transport hub for the area, it would make a good base for touring around. Do you have a nightly budget in euros to better suggest you. But in general, an hotel between the castle and the Place Graslin in the historic center and/or close to the tram line would probably be ideal for you.
In Nantes itself beside the château. You also have the cathedral, the passage Pommeraye and the historic center. Many museums. The machines de l'île. Check out what exposition is held in the LU building plus the view of the city from the Tower is nice.
https://www.levoyageanantes.fr/en/to-see/
As for day trips, east you have access to the Loire Valley with Angers (the castle and the tapestry of the apocalypse) and Saumur being easily accessible. North of Nantes, you have Rennes and Chateaubriant.
https://www.tourisme.destination-angers.com/en
https://www.chateau-angers.fr/en/
https://www.ot-saumur.fr/SAUMUR-VAL-DE-LOIRE-invitation-to-travel_a26018.html
https://www.chateau-saumur.fr/en/
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https://www.tourisme-rennes.com/en/
https://www.brittanytourism.com/destinations/the-10-destinations/rennes-and-brittanys-historic-gateways/rennes/
http://www.tourisme-chateaubriant.fr/en/
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Closer to Nantes, you have Clisson to the south.
https://www.visitnantesvineyard.com/the-destination/the-unmissable/the-amazing-clisson/
Closer to the ocean to the west along the train line from Nantes to Le Croisic you will find : St Nazaire, Pornichet, La Baule, Le Pouliguen, Batz sur Mer and Le Croisic.
https://www.saint-nazaire-tourisme.uk/
https://www.tourisme-lecroisic.fr/en/
https://en.pornic.com/
https://www.brittanytourism.com/destinations/the-10-destinations/brittany-loire-ocean/pornic-and-the-retz-area/
https://www.ot-batzsurmer.fr/
https://en.labaule-guerande.com/la-baule-guerande-peninsula-and-its-surroundings.html
https://www.atlantic-loire-valley.com/atlantic-coast
https://www.levoyageanantes.fr/en/to-do/
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The public transport website for this area : https://aleop.paysdelaloire.fr/
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The TER sncf website offers some deals that might interest you : https://www.ter.sncf.com/pays-de-la-loire/ete-aleop-en-ter
https://www.ter.sncf.com/pays-de-la-loire/decouvrir/balades-plages-en-pays-de-la-loire
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You could also consider Vannes as a nice day trip :
https://www.golfedumorbihan.co.uk/explore/meet-the-exceptionnal/visit-vannes/
https://www.brittanytourism.com/destinations/the-10-destinations/southern-brittany-morbihan-gulf/vannes/
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More information and ideas :
https://www.levoyageanantes.fr/en/by-train-around-nantes/