A local museum is a museum

Museum

A museum is an institution that cares for a collection of artifacts and other objects of scientific, artistic, cultural, or historical importance and makes them available for public viewing through exhibits that may be permanent or temporary. Most large museums are located in major cities...

 that covers local history

Local history

Local history is the study of history in a geographically local context and it often concentrates on the local community. It incorporates cultural and social aspects of history...

. Its collection normally includes objects with a local connection of some sort. Such museums are often small in nature and have a low budget for their running costs. Entry costs are normally low as well.

A local museum covering a city

City

A city is a relatively large and permanent settlement. Although there is no agreement on how a city is distinguished from a town within general English language meanings, many cities have a particular administrative, legal, or historical status based on local law.For example, in the U.S...

 is sometimes called a city museum and a local museum covering a town is sometimes called a town museum.

History

The first suggestion of establishing local museums in Britain was make by William Sharp

William Sharp (homeopath)

William Sharp was an English surgeon and physician. Sharp is credited with first advocating the establishment of local museums in Britain and for putting science on the curriculums of British public schools...

 in the nineteenth century. On the strength of this suggestion he was admitted to the Royal Society

Royal Society

The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...