Are you allowed to investigate locations with no clues?

For instance can I use burglary in the hallway of the house which has an easy shroud but never gets clues?

The investigate action doesn't say you can't but I'm not sure if the rules of the word "instead" need there to be clues on the location to use burglary

Yes, you can use Burglary in a location that has no clues. Don't have active link but this has been answered on arkhamdb.com.

Yes, Burglary works fine on locations without clues. Just keep an eye out for two different triggers. Some trigger after a successful investigation (which work without clue tokens) and some trigger when you would discover a clue (these do not work without clue tokens).

Yes, but bear in mind that investigating a room without clues will not work to remove clues from Cover Up.

The reason why Burglary works with no clues is all it cares is if you successfully investigate. Investigate just means defeat the Shroud in a location, and get a clue if there is one.