Abbaye Saint-Nicolas de Verneuil-sur-Avre
Abbey located in Eure, in France.
Each edition grades its towns against each other only.

All 6 places on the list are châteaux or heritage sites. None of them is inside Bâlines itself. Beyond the town, Cathédrale Notre-Dame d'Évreux sits 34 km away.
Once you have seen Abbaye Saint-Nicolas de Verneuil-sur-Avre, try 5 châteaux.
Best known first: by how many Wikipedia and sister-site articles cover each place (Wikidata’s count). It isn’t a ranking of how good they are.
The map stretches to Château de la Gadelière, 4.7 km away.
The first 20 on the list, numbered as below. The shape is the commune of Bâlines; the orange dot is its centre. © OpenStreetMap contributors · commune boundary: IGN
They are all châteaux or heritage sites: 6 in all.
Dark: in Bâlines. Light: in the communes within 5 km of its centre.
Look within 5 km of its centre for all 6.
Nothing is mapped in Bâlines itself; these are within 5 km of its centre.
Cathédrale Notre-Dame d'Évreux, at 34 km, heads the 12.
AttractionCathédrale Notre-Dame d'Évreux34 km northeast, in Évreux
ChâteauChâteau d'Anet36 km east, in Anet
ChurchChapelle royale de Dreux29 km east, in DreuxChâteauChâteauChâteau de Conches-en-Ouche24 km north, in Conches-en-Ouche
AttractionChâteau de Beaumesnil35 km northwest, in Mesnil-en-OucheAttractionAttractionAbbaye Royale de Saint-Évroult38 km west, in Saint-Evroult-Notre-Dame-du-BoisAttractionAttractionBroussard38 km northeast, in SasseyChâteauChâteauChâteau de Chennebrun16 km southwest, in ChennebrunAttractionAttractionGisacum34 km northeast, in Le Vieil-ÉvreuxChâteauChâteauChâteau de Senonches21 km south, in SenonchesChâteauChâteauChâteau de Saint-Georges-Motel29 km east, in Saint-Georges-MotelChâteauChâteauChâteau de Sorel30 km east, in Sorel-MousselPlaces within 40 km of Bâlines with an article in both French and English Wikipedia, nearest first.
Nothing is mapped in Bâlines itself, but within 5 km there are Abbaye Saint-Nicolas de Verneuil-sur-Avre, Château de Verneuil-sur-Avre, Château de la Gadelière and Château de Montuel.
No museum or gallery is mapped in Bâlines or within 5 km.
The nearest with articles in both French and English Wikipedia: Cathédrale Notre-Dame d'Évreux (34 km), Château d'Anet (36 km), Chapelle royale de Dreux (29 km), Château de Conches-en-Ouche (24 km).
From OpenStreetMap and Wikidata: named museums, galleries, châteaux, abbeys, gardens, zoos, theme parks and other visitor attractions whose mapped point lies inside the commune of Bâlines, then those in the communes within 5 km of its centre, and well-known places within 40 km. Houses, ruins and gardens need a sign they’re open to visitors; places marked private, closed or disused are left out. The historic-monument link is the Culture ministry’s Mérimée record. A place that isn’t mapped isn’t listed, so this isn’t everything there is to see.
Sources: OpenStreetMap (© OpenStreetMap contributors, ODbL), Wikidata (CC0: descriptions, websites, Wikipedia articles), the Culture ministry’s Mérimée database (Licence Ouverte 2.0), IGN commune boundaries. Distances are from the commune’s centre point.
Photos from Wikimedia Commons, each under its own licence (our copy, resized).
Contains public sector information under the Licence Ouverte / Open Licence 2.0 (Etalab): INSEE, DGFiP, the Interior Ministry’s statistics service (SSMSI), the Ministry of Education (DEPP), the Health Ministry’s statistics service (DREES) and the Housing Ministry (Carte des loyers). Commune boundaries: IGN Admin Express.