what exactly is a baxter?

It's the person that is a nice and (typically) good person but is completely wrong for you.

Good example and probably the one Showalter mirrored off of, character wise, was Walter (Bill Pullman's character) from Sleepless in Seattle, hair and everything man.

Just as Elliot was wrong for Caroline. Caroline was COMPLETELY wrong for Elliot.

I saw an interview with Showalter. He said that The Baxter is actually slang for Brooklyn.

I would describe a Baxter (man or woman) who is basically a very nice person, but when it comes to relationships, every time they try to be cool or make a move to create some passion, it just comes off lame, until the person they are seeing decides that, even though the Baxter has some stuff going for them, he/she just isn't the person they want to be soul mates to for a lifetime. I've dated a few Baxters myself, but I'm a good person because I did feel bad when I decided I had to stop seeing them.