If I were re-imagining STAR TREK: THE NEXT GENERATION...
CONTINUITY
I would have set it in the same Universe as TOS, with Capt. Kirk's exploits being part of their history. That does not mean they would've been genuflecting to TOS all the time. Most continuity comes from simply avoiding contradictions with what has been done before. Picard and company would not be looking at a "hole in space" as they did in "Where Silence Has Lease" and pondering it as if nothing like it had ever been seen before ("The Immunity Syndrome").
DIFFERENT TONE
The cast of NuTNG would've been somewhat different than TNG. It's a starship, exposed to hazards in deep space, not a daycare center. There would be a substantial civilian presence of expert astronauts and scientists on board, some of them permanently stationed there, others mission-specific. No psycho-babble from Troi: she would not serve as "ship's counselor", but as the ship's senior civilian scientist and liaison to the captain and XO. And Troi and Riker would not have had a history. Instead, Troi would enjoy being alternately a thorn in the side of the ship's top brass, and being an aggressive team player in getting missions carried out. In essence, Troi is a seasoned professional civilian astronaut and scientist, a driven career explorer, has a long history of rough-riding in space, and she loves her job.
Picard and Dr. Crusher would likely not have a romantic history, but instead may have met on past missions/assignments as ladder-climbing officers. I'm not sure I would want her son aboard.
Tasha Yar would not be a tom-boy stereotype. I wouldn't mind seeing a woman who looks like Denise Crosby (I'd actually love to see a lady champion a revival of Crosby's 80's hairstyle) but I would want to see Yar less as a failed-colony-victim-turned-tough-girl and more like a young, up-and-coming James T. Kirk. I'd want to see her as a command-track candidate, learning the ropes from Picard and Riker. Maybe a little touch of Shelby in her.
Worf and Klingons would have a more alien dimension to them, like Spock had as a Vulcan in TOS. I never liked how TNG made Worf and Klingons out to be some caricature of Gen. Urko from the 1970's "Planet of the Apes" TV show. I would bring some of the characteristics of Klingons from TOS; I liked the kind of cold-blooded logic exhibited by Kor and Kang, kind of like anti-Vulcans. DS9 did a great job making the Vorta, Jem'Hadar and Founders so alien. I would expect the nuTNG Klingons to be the same way. There would be more than one Klingon stationed aboard the Enterprise, but Worf would be the senior Klingon officer aboard ship. (It would be very interesting if Picard would report to a Klingon Starfleet flag officer once-in-a-while.)
It would also be interesting to correct an omission made by TNG's makers early on ("we don't do antenna") by including an Andorian in the the cast of characters.
Picard would be on-track to a fleet command after five years aboard the Enterprise-D. He would not become a permanent fixture aboard the Enterprise, nor would Riker. Both characters would be important, and may appear throughout the series run, but there would be much greater emphasis on the other characters right from the get-go. That's part of TNG's mistake. Patrick Stewart was great as Picard, and that was of course no surprise. But over-emphasizing Picard hurt other characters and the whole scope of the show from the get-go. Witness Yar's and Crusher's departure.
I won't hide my love for Dr. Pulaski. Maybe she should either be CMO over Beverly or be the base CMO Beverly has a regular dialogue with. Pulaski's wit and sarcasm reminded me of Dr. McCoy from TOS, my all-time favorite character in TREK. I liked that Pulaski in TNG was a full commander. That gave her extra clout with Picard, and I really liked how she talked back to Picard right from the moment they met. She came across as a confident, highly professional doctor and command-grade officer who wasn't afraid to speak up when necessary. Having both Kate and Beverly aboard a NuTNG Enterprise-D could present new story opportunities. Pulaski could be a ship-based character, having a close alliance with Troi, while Crusher would be the one who goes on away-missions.
Data would be portrayed by a younger man. Data may be looked upon with some skepticism, and may not be more than a senior lieutenant. I would not be opposed to a nod to Lal, by making the Data character female.
I always had a soft spot in my heart for Geordi LaForge. I enjoyed the whole blind-guy with prosthetic eyes thing. I would be tempted to make him a sighted person with no prosthetic, just a junior officer who enjoys tinkering with technology. (Maybe Geordi got his start in the shipyards, involved in building Galaxy-class starship components.) That's one thing I would borrow from ENT: starship senior-grade officers would have a career history in starship technology, development and construction. One of Picard and/or Riker's previous posts may have been to help supervise the construction of the new, prototype Enterprise-D. (The E-D would be only the second or third ship of her class built.)
I would also like to see the NuEnterprise-D have a port, or ports, of call. Maybe an evolving Space Station K-7 could be one, as a nod to TOS. Another could be a starbase. Picard and his Enterprise would report there occasionally to pick up cargo or new personnel and give their mission status report to fleet command.
The whole '80's actors-and-actresses-in-tights thing would go bye-bye. I much preferred the less-vain-looking jumpsuit uniforms in DS9 and ENT. Troi would wear either a plain uniform or 24th century business attire. No catsuits, please.
(SOMEWHAT) DIFFERENT SHIP
Also: when it comes to style, no fake bark on the ship, please. I agree that the E-D main bridge did look a little too much like a hotel lobby. Viewers and the cast deserved better.
And the ship should've had a better design as well. There were elements of both the Enterprise-D and -E that I liked. The best-looking ship in TNG never made a direct on-screen appearance, though.
Probert's forgotten Enterprise-C looked more interesting. The NuE-D would need better embarked craft. TNG's shuttles looked wimpy in my opinion. One thing VOY did right was give us the Delta Flyer. NuE-D would need a better-looking and more usefully-designed fleet of shuttles and runabouts. The undercut on the underside-aft of the secondary hull would also serve as a docking port for an escort-type mini-starship like the Defiant. Having an escort that could go on long-range away-missions would open up numerous story possibilities. It would also give the Galaxy-class starship a better military stature.
The Galaxy-class starship herself would be similar, but it would have a shape that would borrow a little from Kirk's Enterprise. The nacelle pylons and secondary hull especially. I preferred the glowing nacelles of the TNG Enterprise over the TMP refit, but the blue wraparound grille on the E-D was overdone. Too much eye candy. Tone it down. The ship's hulls also looked pock-marked with too many windows. And I liked the original E's glowing saucer domes and block-lettered hull nomenclature much more.
STORY ARCS
To cement a different tone into place, there would be greater in-series continuity. I would want to see STARGATE SG-1-style story arcs. Q would be one coherent story arc, but it would be portrayed by more than one actor. Q might only appear once every two years. The Borg and Romulans would be there, but they would be used more wisely. They would not be one-dimensional aliens that appear gratuitously once every so often just to give the cast heartburn. They would have story arcs and their place in the NuTNG universe would have purpose. They could be a security threat, but the stories would give them motive, not just a mindless appetite for body-count. I was intrigued by the brief appearance of the Husnock in
"The Survivors". Too bad they were all killed off. Thier use of anti-poroton beams seemed to link them technologically to the builders of "The Doomsday Machine" in TOS.
A potentially extremely interesting story arc would have the NuE-D discover a stable wormhole to a distant galaxy or another universe entirely, and Picard and company be assigned to explore where the wormhole leads and report back. And what if they find more Husnock or Planet Killers there???
There are elements of TOS, TNG, DS9, ENT and maybe even VOY that would be great fun to explore in a TNG reboot. More on this later.