I think the question of 'who' is just as important as the question of 'where' when contemplating a new Star Trek. TOS, TNG and DS9 are the shows which most people seem to consider the best, including myself. These shows worked so well because the feel of the show and the rest of the crew were all worked around the captain, who provided a kind of centre around which everything else developed.
TOS was about exploration, about going boldly where no man had gone before. Kirk was the ideal captain, he embodied this tone. Kirk was a man who could fly by the seat of his pants and enjoy it, the crew reflected this. Spock was the perfect right hand man for Kirk because he was so unemotional and thought everything out rationally and logically. Bones was a perfect foil for Spock and friend for Kirk because he was very sentimental. Spock served to show Kirk his duty, and how to do most good for the most people. Bones was someone who could speak frankly to his captain, and really remind Kirk of the consequences of his actions. Kirk was a mans man, and the Enterprise was a 'mans ship' without luxury.
TNG was far more about Enterprise being the flagship, it was often involved in first contact situations, or mediating relations between different species. Picard was the perfect captain to centre the show around. He was a born diplomat, a man who would gain victories from diplomacy, legality and morality, and a man who followed orders almost without question. His two right hand men were Data and Riker. Riker was perfect as the 'mans man' to Picards intellectual, he was a born first officer, the perfect mediator between crew and captain, since Picard was quite removed from the crew. Data worked as well as he did because he constantly forced Picard to think about what was human.
DS9 was about being in a situation removed from Starfleet, where TNG needed a man who knew how to use law and reason, DS9 required a man who knew how to use force. Sisko is perfect because he is a damaged man who comes to a damaged station, orbiting a damaged world. DS9 was about making tough choices, that may not be totally moral but that were necessary. Sisko would follow his heart, and thats what this show needed, he was also a man who could get along with just about anyone, important for a space station. The crew, too, were characters who largely had to cope with diffcult new circumstances: O'Brien with his new senoirity, Worf with being in a civilian atmosphere, Dax in a new host, Bashir learning the realities of 'frontier medicine'. Kira was a great right hand 'man' for Sisko because she was basically going through the opposite experiece. She was a freedom fighter, she had to do bad things somethings, but they were always for the greater good. She now has to deal with being part of a large, often beaurocratic organisation.
Even the main villains were centred around the captains, in DS9 and TNG. The Borg are relentless, you cant talk and negotiate with them, the perfect challenge for Picard. The Dominion, though sometimes violent, mainly trys to invade the alpha qaundrant through political manipulation, alliances and treatise, the perfect challenge for such a passionate leader as Sisko.
In VOY, the most glaring problem was Janeway. She didnt have any particular character strengths, and more importantly she didnt have any exposed flaws. She just did what she did and it turned out to be right because the script was written to make it right. She didnt reflect the situation at all, and niether did the ship and crew. They still had the holodeck, for crying out loud! Id like to see a show which is basically Voyager done well.
Both Voyager and Janeway were really built for science. Janeway was an officer who had never really needed to make tough decisions before, the ship was built for scientific research, not action. Most importantly, neither captain or ship were picked for this situation, they were stuck in it. Janeway should have been a somewhat weaker character, someone who was inexperienced, but who was guided through situations by a solid morality, and by the help of those around her. Early Voyager episodes could have concentrated on Janeway making mistakes that cost lives, and actually make her reflect and grow from these experiences. She could even have felt it was a mistake to blow up the array, her guilt could have been a major theme. The character of Chakotay should have been a character who was used to using force and going in all guns blazing, he could have made a good foil for Janeway, and, as she learnt from his approach, he would learn how to curb his aggression. Tuvok would have been good as he was, but with a flawed Janeway he could have been a more integral advisor, especially so far away when they really do need to be rational. The crew of VOY was so dull because they didnt relate to the captain or situation. The journey of Voyager would have been adapting quickly to circumstances that the crew were never supposed to face.
I dont know how this could be done without being an obvious touch up of VOY, but thats what I would like to see. A situation where the captain doesnt have the experience, but needs to learn fast to cope with new realities, and really needs to learn from his mistakes. I know it will be ridiculed, but I imagine someone like Niles Crane, a man or woman who was so NOT made for this task, but has this task thrust upon him, put in a situation where he isnt just at a desk, but where his desicions cost lives, and hes there to see the bloodshed. Where the ship cant support holodecks or replicators, where theres nothing to distract the crew from going stir-crazy. Testing out the starfleet ideals in a place far from starfleet on the edge of total desperation. I think this would really emphasis the humanity that is so present in good Trek.