For some of the options discussed here, you need Tinycore version 3.6 or higher.
For a list of mirrors, see mirrors.
To have a list of mirrors to choose from, install mirrors.tcz.
To select a mirror, open the App Browser, and click Mirrors, then select a mirror.
If you have a local mirror, or want to use mirrors not listed in mirrors.tcz, create a file /opt/localmirrors, and list them.
To find out your existing mirror, open the terminal and type
cat /opt/tcemirror
To select a mirror, use
tcemirror.sh