I would like to see more "going where no one has gone before". Let's skip a couple of decades past STO to the mid-25th century, where the Federation has developed Quantum Slipstream Drive to the point that it can be used for intergalactic travel, and focus on a ship (or small task force of ships) that is sent out on the Federation's first foray into another galaxy--the Large Magellanic Cloud. Call the series "Star Trek Magellan", and name the main ship the Magellan as well if you need a catchy sounding name.
How many Starfleet Engineers does it take to exchange an Anti-positronic Photon Emitter?
I personally feel that Star Trek is supposed to be set specifically around the Federation because ST is all about Humanity's voyage into growth. Though one darker side of the Federation is Section 31, which is intriguing to me. They could have a series set around Section 31 headquarters, hidden clandestinely on a colonial facility on some planet where no one would build a facility.
They could have an experimental Federation ship they use on their missions. I think it would be cool, kind of like Star Trek meets a blend of "James Bond" and "Nikita." That would make for something people would want to watch, with espionage, action, conspiracy, and Orion females. I would have set during the current Iconian Wars.
"Star Trek: Rubicon" Season 1, Season 2 A new era, a new time, a new crew, a new ship, a new mission...
"I rather believe that time is a companion who goes with us on the journey and reminds us to cherish every moment because it will never come again."- Jean-Luc Picard
My idea for a Star Trek series would be set after Nemesis, have a new crew take over the Enterprise E that way we get old casts make guest appearances, storyline set in between Nemesis and the events of what happened in Star Trek 11. The other idea I have is make a Star Trek series set in the STO era. My third idea is have a series set after the events of ST09 but before STO era. Fourth idea, have the series set in Daniels future maybe. Personally should do this one later after the other series which continues the prime-verse storyline.