It is typical of online presentations that a library would place a more complete, annotated or transcribed edition of a manuscript online for the public perusal while a museum is concerned with a more holistic representation of manuscript, along with timelines or contextual notes. These museums, though sometimes working hand in hand with libraries to produce digitised versions of their holdings, are no exception.
The Metropolitan Museum of Art, NY: The Cloisters
The Met houses an unique department called The Cloisters, which preserves medieval sculpture, stained glass windows, artefacts, and a plethora of other items. Within this department there are several exhibits on manuscripts; they hold the Book of Hours of Jean D’Evreux, the Belle Heures de Jean de Berry, and a leaf from a Beatus manuscript.
The Fitzwilliam Museum
This museum in Cambridge places selections from the Macclesfield psalter online in high resolution, accompanied by several articles about it that describe the history of the book, its value, and what makes it unique.
The Pierpont Morgan Museum & Library
This museum has put up a great many manuscripts for public viewing online with a feature that allows you to zoom in on the manuscript in question, but these manuscripts are only selections and not whole works. That in mind, enjoy the high resolution and incredible detail of these manuscripts.