EMILY: Well, I visited the family mausoleum today … I just wanted to check on things, make sure they were keeping it up, changing the flowers, you know.
A mausoleum is a building which contains a burial chamber with spaces for the dead to be interred. They have existed since ancient times for rulers, the nobility, and gentry, and became particularly popular in Europe and its colonies in the 18th and 19th centuries as burial options for the wealthy.
In real life, Cedar Hill Cemetery in Hartford [pictured] has mausoleums for burials, usually owned by wealthy and prominent families, many of them of historic significance. The Gilmore family mausoleum is presumably one of them.
The Annotated Gilmore Girls 