Kate wasn't avoiding Sawyer. Of course not. She'd just learned to depend on herself and only herself thanks to her life before crash landing on the island. Even once she was on the island, trust was more out of necessity than anything else and while Kate thought a handful of the people from Oceanic Flight 815 might be trustworthy, there were still some that she hadn't figured out yet.
Sawyer was one of those people. She hadn't quite determined whether he'd be an ally in a bad situation or whether he'd tuck tail and take care of himself and only himself.
Going to The Ratcatcher Inn was more about getting a drink and getting away from all the weirdness of this place. Now that people were passing out and walking around like they were possessed, Kate didn't know how much she wanted to get involved. She was sure some protective instinct had the potential to kick in if she actually saw someone in danger but for now, she just wanted a drink and a break. Sawyer just happened to be there and she figured that, at this point, he was the best ally she was going to get here so she might as well just come to terms with it and deal.
Slipping into the seat next to him, Kate leaned forward on the bar with her elbows. "Hey, stranger."