I like Niloc's idea (I think it was him) of having a series that is the generation after TNG. Let's go forward in the timeline instead of continually going to the past.
Yeah, that's definitely what I'd like to see. Tech and TV production values have increased to the point where they could easily make a series that was convincingly further in the future than all the TNG through Voyager shows were.
We've had a ton of both post-apocalyptic stuff, and serialized stuff (and I like both of those when they're done well) - could really use at least one show that has a hopeful, optimistic future, and it wouldn't be a bad thing if most episodes were stand-alone rather than serialized too, or a mix of both.
Shake it up a bit by maybe making relations with the Romulans better in the future - how about a Romulan first officer/science officer instead of a Vulcan? Similar to how Worf was the first Klingon in Starfleet.
edit: TNG series with Patrick Stewart? Why the fuck would Picard still be a Captain at this point? With Kirk having him demoted from Admiral for being a jackass made sense, but Picard?