I'm using a local gitweb instance for this purpose. I have a directory of favorite repos cloned using "git clone --mirror" and a cron job to sync them every 3 hours. gitweb provides a web interface for browsing them.

I like that it lets me open files without JavaScript enabled and search the code without logging in. I still use GitHub.com to read the issues on a couple repos though.

Example of what gitweb looks like: https://sourceware.org/git/ - There's also cgit which is similar: https://git.kernel.org/