Whether you can hide the tags without hiding other things such as date, author, comments link, is theme dependent. Some themes lump things together as you have found. On themes that lump things together, there is no way to separate them out without access to the underlying theme PHP files, and we do not have access to those.
Your best bet is to look at other themes and see if you can find one you like that does not lump them together.
If you are using firefox, then the firebug or aardvark firefox addons help tremendously in figuring things out quickly.