Chemin de fer touristique Pontarlier-Vallorbe
Railway museum in France.
Each edition grades its towns against each other only.

All of it lies outside: 4 places within 5 km of its centre, none in Montperreux. Among them are a museum, a manor and a fort. A day out reaches Fort de Joux, 5.7 km away.
Chemin de fer touristique Pontarlier-Vallorbe aside, the next best known are a manor, a fort and an attraction.
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.
Of the 4 nearby, most are to the south.
The first 20 on the list, numbered as below. The shape is the commune of Montperreux; the orange dot is its centre. © OpenStreetMap contributors · commune boundary: IGN
It comes down to a museum, a manor and a fort.
Dark: in Montperreux. Light: in the communes within 5 km of its centre.
4 places make the list, every one within 5 km of its centre.
Nothing is mapped in Montperreux itself; these are within 5 km of its centre.
The history of Montperreux → · Parks and trails in Montperreux →
Allow a day for Fort de Joux, 5.7 km away, the pick of 5.
MuseumMusée Courbet34 km northwest, in OrnansChâteauChâteauChâteau de Cléron36 km northwest, in CléronAttractionAttractionChâteau de Syam33 km southwest, in SyamAttractionAttractionForges de Syam33 km southwest, in SyamPlaces within 40 km of Montperreux with an article in both French and English Wikipedia, nearest first.
Nothing is mapped in Montperreux itself, but within 5 km there are Chemin de fer touristique Pontarlier-Vallorbe, Maison de Monte au Lever, Fort Lucotte de Saint-Antoine and Fontaine Ronde.
One, in town or within 5 km: Chemin de fer touristique Pontarlier-Vallorbe.
The nearest with articles in both French and English Wikipedia: Fort de Joux (5.7 km), Musée Courbet (34 km), Château de Cléron (36 km), Château de Syam (33 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 Montperreux, 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.