Wow; a very interesting question, with many possibilities! For me, i would like to see any of the following:
(1) Daily life in a federation colony - either a colony at the core of the Federation, or a colony on the edge of Federation space, e.g. on the border with Romulans, Cardassians, Klingons, Tzenkethi, etc.
(2) The investigation of lost civilization - as a someone who studies ancient history, I would like to see a team of Federation or Starfleet scientists, archaeologists, and historians investigate a lost civilization, e.g. the Ikonians; and basically investigate the 'true' final frontier: time, and learning something about their own society in the process. Maybe they could discover something important for the future of the Federation, like a new technology of space transportation - e.g. the 'stargates' of the Ikonians.
(3) The rise of the Cardassian Empire - an exploration of what the Cardassians were like before their imperial ambitions, including - maybe - their early interactions with Bajorans. And we see how the military slowly began to take over the administration of Cardassia, introduce new doctrines, and begin their expansive period.
(4) The 'bottom of the class' starship - we always see those starfleet crews that are 'the best of the best'; what about those who graduate bottom of the class. They would be like underdogs that Starfleet, etc, would not really give a chance to be at the forefront of space exploration. What would life be like for them? I have an image in my head something like the English show - Red Dwarf - where characters are constantly trying to prove themselves and get promoted, or stumble their way through situations. Hopefully we could have a fun show, without actually making fun of these people for being near 'the bottom.'
My last idea is one that is quite personal to me. I come from the Eastern Mediterranean/Middle East and I would like to see a standard series, set on a starship, exploring the galaxy, but the crew comprises of Greeks and Turks, Arabs and Jews, Saudis and Iranians, etc. For me, it would help share the hope I have that in the future this part of the world that has seen so much war, death and hate, finally achieves peace. All these peoples that once hated each other, can now work together, and achieve things that once seemed impossible.
Thank you for reading my post, and I apologize if any of my English was strange - English is not my first language
