I have two answers, depending upon who is making the series, and how they approach and understand Tolkien's work.
If someone took a "Peter Jackson approach" - that is, not inserting themselves into it too much, but trying to adapt Tolkien and his ideas as faithfully as possible - then I'd love to see a full-blown Silmarillion series, or rather the Quenta Simarillion, aka the First Age. Maybe something like this:
Option One: Silmarillion Series
First season: Prologue depicts the Ainulindale, and the major events of the Years of the Lamps and Trees...would be hard to do, but with the right director could be really cool. The season proper begins with a supposedly-repentant Melkor being released by the Valar, the forging of the Silmarils by Feanor, the conflict among the elves, then Melkor stealing the Silmarils and Ungoliant killing the Two Trees. The season focuses on events in Aman, and culminates with Feanor leading elves to Beleriand, and then being killed by Balrogs. Ends with Fingolfin leaving Aman for Middle-earth.
Second season: Prologue depicts creation of sun and moon, awakening of Men, and establishment of the kingdoms of the Eldar in Beleriand. The main narrative starts sometime later, with Morgoth under siege in Angband for several centuries. Depicts arrival ("first contact") of men, and dwarves, and their alliance vs. Morgoth. Dagor Bragollach. Ends with death of Fingolfin.
Third season: Focus on men: Hurin and Huor, and then Beren and Luthien, and culminates in the fifth battle (Nirnaeth Arnoediad).
Fourth season: Focus on Turin and Tuor, fall of Nargothrond and then culminates in the fall of Gondolin.
Fifth season: Later years of the First Age. Earendil and the War of Wrath. Destruction of Angband. Ends with Morgoth being cast into the Void.
Or something like that! It could possibly be done in three 10-episode seasons, too. Oh, and no hobbits!
Option Two: Other Possibilities
Barring someone like Jackson, either another Amazon-esque series or studio who is less concerned with or capable of a faithful adaptation, a few ideas that come to mind:
Angmar: A series depicting the war between Arnor and Angmar and the Witch-king.
Dragons: A series focusing on the fight against dragons by the dwarves and men, in particular. The dragon Scatha could be central. Set around the same time as the above (1500-2000 TA), so could be combined.
Middle-earth: The Fourth Age. One of the great literary losses of the last century is that Tolkien didn't complete (barely started, really), his follow-up to the Lord of the Rings: The New Shadow. Evidently he didn't write more than 13 pages because it was just too depressing. Anyhow, I'd fast forward from LotR by at least a couple hundred years, maybe longer. Make sure all the canonical characters are dead or have passed over to the West, and then create new characters, with some new evil arising - perhaps a cult of Morgoth, or maybe another Balrog turns up, or one of the blue wizards comes back and is set on domination. Elves are dwindling and diminishing, dwarves becoming more insular. Etc.
The Blue Wizards: An entirely new story about the blue wizards in the East...there is so little written about them, but they remain a fun mystery, and at least the show-runners would have greater freedom to explore different stories and ideas. Maybe one becomes evil, and the series focuses on their fight against each other.
One final note: No Tom Bombadil. While I felt his (and Goldberry's) lack in the LotR films, I have since come to feel that it was probably for the best. Tom Bombadil is inherently an enigma - whether he is a Maia, Iluvatar itself, Tolkien inserting himself, or just an odd-ball, he is probably best left unexplained and un-depicted (that said, I would have liked to see Robin Williams in the role).