The answer is
You rolled double 6's for your opening roll on a game of Monopoly.
First is a dive; not much, but it's cheap
Mediterranean Avenue: The cheapest property on the board, named after the Mediterranean Sea, where you can dive.
Next is the cache for society's keep
Another dive follows; it's much like the first
Baltic Avenue: In the same set (dark purple) as Mediterranean; it's also named after a body of water that you can dive in, the Baltic Sea.
Please not the next one; of all, it's the worst
Luxury tax: Pay 10% or $200 (in the U.S. at least)
The next is for readers, they'll chew and they'll chew
Reading Railroad: "Chew" sounds like a train: "Choo choo"
After that, east; you're light but you're blue
Oriental Avenue: "Oriental" means "eastern". Part of the light blue set.
The next's rather risky; there's some good at least
Chance: Could have a positive or negative outcome.
Then two more are stately, and much like the east
Vermont and Connecticut Avenues: Both part of the light blue set as well, named after U.S. States.
Next comes the crooks while they go round the bend
Jail: On the corner, while you're going "round the bend" is where the "crooks" are.
Then comes a saintly and violet friend
St. Charles Place: Starts with the word "Saint"; part of the light purple (violet) set
But I got the highest, as high as one gets!
I rolled a 12 right off the bat; you can't roll higher than that in Monopoly.
I now have to go there, so tell me: what's next?
The next property on the board is Electric Company, the 12th space from "Go".