Use HTML Tidy to just indent HTML code?

Use the indent, tidy-mark, and quiet options:

tidy \
  -indent \
  --indent-spaces 2 \
  -quiet \
  --tidy-mark no \
  index.html

Or, using a config file rather than command-line options:

indent: auto
indent-spaces: 2
quiet: yes
tidy-mark: no

Name it tidy_config.txt and save it the same directory as the .html file. Run it like this:

tidy -config tidy_config.txt index.html

For more customization, use the tidy man page to find other relevant options such as markup: no or force-output: yes.