So I'm going to answer the question "favorite" TV fathers rather than "best" TV fathers. "Best" requires so much more justification that I quite frankly don't have. "Best" says something more than "favorite." "Favorite" is a very personal opinion of quality. "Best" is a much less personal opinion of quality, it implies something broad that "favorite" does not.
That said, Bobby (Supernatural) is one of the best father figures I've seen. He's always there for his boys without question, despite them not biologically being his children.
Comedy shows might get overlooked here... but Bobby Cobb (Cougar Town) is also a really amazing father. He doesn't always get it right, but he tries. He really loves Travis and you can see that in everything he does. I admire him for never bailing on Trav ever. Part of the tragedy of Bobby's character is that he's so socially f***ed up... But the beauty of his character is how much he tries and how much he loves. He loves Travis more than anyone and anything. He named his dog Travis because he missed his son. One of the most touching moments of a VERY touching show.
Keeping with the Bill Lawrence... Dr. Cox is a really wonderful father. And the beauty of including Dr. Cox in this list is he's not just a good dad, but he's a good father figure to JD. He's mean to JD, sure. But he genuinely cares for him and gives him the pushes he needs to become the doctor and more importantly, the man he becomes. He's also a good dad to his children. He spends the whole night one night looking for someone to give his daughter a shot because he doesn't want her scared of him. And I'll never forget the moment when Jack asked where babies come from and Dr. Cox said "well sometimes when a mommy and a daddy love each other very much... they close they eyes, and they make a wish." I'm tearing just thinking about that moment.
All of the fathers of Modern Family make this list. Phil, Cam, Mitchell, and Jay. Honestly, I don't even think this needs any sort of justification because if you've watched even an episode you would see ho much the four of them do for their families. How much they do for all of their children. I will point out Phil and Jay in particular just because their role as father has been more focused on than Cam and Mitchell... but all four are really wonderful. Phil's reaction to the news that Haley is no longer a virgin was phenomenal. Haley didn't see what we got to see because of the show's mocumentary format... But that little speech he did at the end of that episode... That is how every good father should react to that news. And the way Jay has taken in Manny. There is no one moment I could point out for this. There is only the whole show.
Baze (Live Unexpected) is also a personal favorite. When the show starts, he's a complete mess. But he COMPLETELY turns his life around for Lux. From the moment she shows up at his door and tells him who she is, she becomes his world. To me, that proves that had Kate told him of her existence in high school, he would have done everything he could to take care of Lux. Lux was never a burden on him... she was never something he wished hadn't have happened.
Zeke (Parenthood) is a wonderful father and an incredible grandfather. He makes a lot of mistakes, and he's not my favorite character by far. But his children and grandchildren are the most important things in his life. This is another one where I don't have one moment... but rather the whole show.
Burt Hummel (Glee). I don't like to give Glee credit for much of anything... but Burt is such a wonderful father. To both Kurt and Finn. It's remarkable really. This is another one... there's no one big moment to sum it all up. There is only the whole show.
Honorable mentions:
Cal Lightman (Lie to Me). He doesn't make the list because it drives me crazy how he reacts to his daughter having birth control. Not even being sexually active... just having birth control. However, that ridiculousness aside, he's a wonderful father. He adores his daughter and is always there for her. She is is first concern. He's a very intense man, and his parenting is not an exception to this... but he is a wonderful father.
Booth (Bones). He'd be on the list had it not seemed he forgot all about Parker in season 7. The fact that he hasn't once mentioned him and we're 7 episodes in... The season has been focused on his role as father to the new baby... however, Parker seems to have not even been in Booth's mind but fathering seems to be the only thing he thinks about. That said, all the way through to the end of season 6, we've seen him be a wonderful father to Parker. The best dad he could be.