I'm aware there is a speculation thread but I am interested in getting some attention aside from a single post.
I predict that the next Elder Scrolls game will take place about 10-20 years after Skyrim., in a combined map of Valenwood and Elsweyr.
The Skyrim Civil War reaches a stalemate, where it is split into two separate states, with an uneasy cease-fire.
The Dragonborn fades from public attention, although the Blades remnants are still searching for him/her.
Thalmor activity on the southern border of Cyrodiil arouses the anger of local counts/rulers of the southern cities, who send their own coalition of troops to establish a presence around the border region of the Valenwood/Elsweyr to try to block out Thalmor activity. The Emperor denies involvement but declares that the local authorities can react in defense. There is an ongoing debate over this, with the Emperor ultimately trying to prevent all-out war.
Meanwhile, Valenwood is suffering drought and many plants and trees are dying. Many Bosmer are trying to find out why, some ask the Thalmor for help or blame the Thalmor.
Elsweyr isn't fairing any better. The debate over the successor to the Mane, which was already heated with the assassination in the early part of the era and the split of the Confederacy, becomes chaotic with the recent appearance of a Third Moon (which according to legend, signifies the birth of a new Mane).
The player character starts as a captive of a Thalmor patrol along the border of Elsweyr, near the city of Dune, The PC escapes along with a crafty Khajiit friend.
The rest I can't really predict too well but it may involve traveling to the Moons from time to time and perhaps some special Moon Sugar or Moon Shards that grant powers as a gimmick.