This is what I would like to see happen:
Season 7
1. Dany conquers the South, takes the Iron Throne. Tyrion kills Cersei (Valonqar prophecy fulfilled). Jaime is captured and Tyrion convinces Dany to spare him and allow him to fight for them, adding the Lannister banner to her ranks.
2. Arya meets up with the Hound and then Melisandre. The three go to King's Landing and are there during the invasion. The Hound finally gets his chance at revenge on his brother, the Mountain, when he encounters the Mountain under the city attempting to set off the wildfire. Both are destroyed by the wildfire, but Melisandre uses her magic to contain the blast as her final sacrifice for the Lord of Light. Arya witnesses Tyrion kill Cersei. She escapes, but it's unclear where she is going.
3. Jon prepares the North for the White Walker invasion.
4. Bran returns to Winterfell and reveals the truth about Jon. Bran has a vision about Tyrion's true parents (Mad King is his real father, making him a Targaryean).
5. The Wall comes down and the White Walkers arrive.
6. Jon and Dany form an alliance. Jon denounces any claim to the Iron Throne, but remains King of the North.
7. Bran reveals the truth to Tyrion.
8. Sam returns with knowledge of how to defeat the White Walkers using the Horn of Winter.
Season 8
1. Jon, Dany, and Tyrion ride the three dragons leading their combined forces against the Night King and his White Walker army.
2. Jon uses the Horn of Winter to defeat the Night King. The Night King retreats and Sam reveals how to repair the Wall.
3. With the White Walkers defeated, Jon returns to Winterfell with Sansa and Bran. Sansa turns Littlefinger down again and he heads back to King's Landing. Sam is named head of the Night's Watch.
4. Dany and Tyrion return to King's Landing. Dany decides to return to Essos and marry her true love Daario and rule from Mereen. She leaves the Iron Throne to Tyrion, who names Jaime his Hand. Littlefinger becomes his chief advisor (as he continues to plot to gain the Iron Throne).
5. The series ends with the known world ruled by three Targaryeans- Jon in North Westeros, Tyrion in South Westeros, and Dany in Essos. Thus the three headed dragon rules the world.
Probably forgetting something key, but that wraps everything up nice and neat. Not Martin's style, so it probably won't end up that way.
But that's what I would do.