Upon first arriving in Kneece I usually do a lap around the town, clearing out all the buildings. There's a variety of Giant Lizards and Fire Lizards here, as well as a Drake in the central building to the south, and a Salamander in the second building to the north on the west side.
Once you've cleared all the buildings go through the entryway into the big central section. The entryway is right near the southwest corner. The passage around the southeast corner is blocked by two Force Barriers, which require Dispel Barrier Lv.2 or a Piercing Crystal to get through. The northwest corner has one Force Barrier and one Fire Barrier. Fire Barriers can be walked through, but they do damage.
Once through the barriers head to the northwest corner to find another entryway. This requires you to walk through an energy field, but I've never found that it does anything harmful.
Now you have to go into the building in the center. This is the home of Purgatos the mage. If you know the location of the Filth Factory, which you find in the home of the Friendly Roaches, Purgatos will give you the Phoenix Egg. You need this to destroy the Filth Factory.
There's also some research tomes in his bedroom which you can steal, but his pet lizard has a tendency to follow my party around, so I have to be quick in closing the door or it will come into the bedroom, preventing me from taking the books. Don't go near the bookshelf in the main room, as it gives you a splitting headache, due to a trap on the books.
Now you can either go to Shayder and begin the Roach Quest, which is actually already half done, now that you have the Phoenix Egg, or you can finish exploring the Isle of Bigail first.