Which scene in the novel does the best to develop a sense of time and location?
I think Chapter 12, which is entitled “Better Let Blame' Well Alone” is a good indicator of time and location. Huck and Jim are on the raft, and they are floating down the river with Illinois on one side and Missouri on the other:
When the first streak of day began to show we tied up to a towhead in a big bend on the Illinois side, and hacked off cottonwood branches with the hatchet, and covered up the raft with them so she looked like there had been a cave-in in the bank there. A towhead is a sandbar that has cottonwoods on it as thick as harrow-teeth.
We had mountains on the Missouri shore and heavy timber on the Illinois side, and the channel was down the Missouri shore at that place, so we warn't afraid of anybody running across us.
So this tells what place they are in. Huck says that on the fifth night, they passed right by St. Louis and he tells how he would slip ashore and "borrow" some melons or pumpkins or corn from some farmer for food -- so you know that it is a rural setting, probably in a time before modern industrialization.
Also, at the end of this chapter, they see a steamboat, so this is another indicator of time. Steamboats were only in use until the second half of the 20th century, so this places the novel as far as time as well.
You can read this chapter here on enotes and see if you agree with me.