Applying to the JET Program -Vlog #4 - picking your location

yes - in my part of Shimane, the local dialect is called "Izumo ben" but it seemed that only older people really spoke it with any regularity.

One thing I'm afraid of is going to JET and picking up an obscure dialect of Japanese. Thus, I would like to be stationed in an area without a dialect. But if my current "standard" Japanese were not to get muddled with another dialect, thus making me able to speak two dialects, that'd be even cooler.

Izumo is probably semi-rural, but it's the exception in Shimane, other than Matsue. Most places in Shimane would be considered rural.
Semi-rural would perhaps be locations in Hiroshima ken, for example, that while rural in and of themselves, are still very close to a big city like Hiroshima.

in my main JET playlist I have a vlog titled "Money" that covers this topic in more depth.
I brought about $1000 with me when I first came to Japan, and that just about lasted me until I got my first payck.

Sure - there are plenty of private language schools in/around Tokyo that hire foreign teachers.  Just check the internet for job listings and salary ranges.