The origins of Río Grande date back to an era where the culture of the Selk'nam natives, the gold diggers, the great ranchers of Patagonia and the missionaries of the Salesian Order all converged in the same place. 
A walk through the center of the city allows you to appreciate the architecture of early times, reflected in the houses of the historic center.
During the walk you can visit the Almirante Brown Square, the old Water Tower, have a coffee at the popular "Roca" Bar or visit the museums listed below:  

Virginia Choquintel Municipal Museum

Inaugurated in 1992, this museum is dedicated to spreading the history of the northern part of the island.  It has a library and a collection of regional themes covering Aboriginal History and Culture, Contemporary History, Fauna, Flora, Oil Exploration and the First Airline. 
Its facilities also house an Art Room and a small cinema.

Monsignor Fagnano Museum

The building where this museum is located was declared a Historic Monument  in 1983. Visitors can explore the history of the Salesian Order on the island since 1893 and learn about the life and work of Monsignor Fagnano and his interaction with the native tribes.  
The historic Candelaria Chapel, inaugurated in 1899, the Mission House, dating from 1897, the historic cemetery, machinery, vintage carts and a space dedicated to natural sciences can be visited by the public. 
More information at Monseñor Fagnano Museum   

Fuegian Museum of Art 

This museum is located inside the facilities of the Yaganes Cultural Center. Its main objective is to protect the Provincial Art Collection in order to offer the community the possibility of knowing the local artistic production.  
In its three halls there are exhibitions of photographs, paintings, works of provincial artists and guest artists of regional and national level.  
More information at Museo Fueguino de Arte 

Zona Norte Visitors Center

Another proposal related to the history of the place is the Northern Area Visitors Center which offers a self-guided tour, with models and infographics. It is located inside the Yaganes Cultural Center.  

Malvinas Argentinas Museum

Inaugurated in 2014 by the Association of Veterans of Río Grande, the Malvinas en la Memoria Exhibition Hall offers a tour that covers the main events of the conflict, and how it was experienced by the locals. It also has an exhibition of military artifacts and memorabilia. 
For those interested in the history of this conflict, along the Héroes de Malvinas Avenue there are a series of commemorative monuments, located in front of the barracks of the 5th Marine Batallion.