The Katana is the best melee weapon in Project Zomboid. It is a very rare item and your best bet to find one is in boarded up survivor house.
After 60 days Katanas can also be found embedded in Zombies.
Survivor houses can be identified by boarded up windows and doors. They typically stash weapons and canned food. If you’re lucky you’ll find a Katana.
The Katana is a very rare weapon, it’s not really something you can look for. You might come across one but if not there are plenty of melee alternatives that are much easier to find.