sql server express localdb.msi offline installer
Go to this page: https://www.microsoft.com/en-us/sql-server/sql-server-editions-express
Click the download link to download and launch the 5 MB installer.
In the Installer, select "Download Media"
Direct URL: https://download.microsoft.com/download/9/0/7/907AD35F-9F9C-43A5-9789-52470555DB90/ENU/SqlLocalDB.msi
Direct URL for SQL Server 2017 LocalDb: https://download.microsoft.com/download/E/F/2/EF23C21D-7860-4F05-88CE-39AA114B014B/SqlLocalDB.msi
**UPD 2019-03: Current LocalDB version has a bug which can be fixed by installing the latest Cumulative Update (CU)
for those who seek 32 bit edition localDB for download, here it is:
http://download.microsoft.com/download/8/D/D/8DD7BDBA-CEF7-4D8E-8C16-D9F69527F909/ENU/x86/SqlLocaLDB.MSI