Can I check how much space my indexedDB is taking up?

There is not currently a standard (or even non-standard) API that gives a breakdown of storage usage by type.

• In Chrome's DevTools, the Application tab provides a breakdown of storage by type; click the "Clear storage" view in the top left and a graph should appear. This is useful for local debugging, but not understanding storage usage "in the wild"

• There's some discussion about extending navigator.storage.estimate() with this data at https://github.com/whatwg/storage/issues/63

UPDATE: navigator.storage.estimate() now provides a breakdown (in Chrome 75 and later) by storage type.