I really like David Letterman's channel which mostly features archival clips but also had new material where Letterman chats with his longtime producer Barbara Gaines and increasingly with Paul Shaffer as well. It's mostly Letterman telling anecdotes much like his desk monologue segments which were the best part of Late Show.

Interestingly, the channel includes clips from NBC's Late Night despite Letterman's intellectual property dispute with the network, so the two sides must have come to some sort of licensing agreement allowing Letterman to use his NBC material - something he generally wasn't able to do when his CBS show was on the air.

Conan has a similar channel for his archives (including his NBC material, despite his dispute with the network)

I wonder why Leno hasn't created a similar channel for his Tonight Show archives?

And those who have OTA capability should know that Carson airs every night at 10 PM on Antenna TV, shown here on subcarrier 2.2 over WGRZ.