What are reasonable areas to live in Bangkok with respect to nearby employment?
For example, Silom is the manufacturing district. What other places might I chose to live in to be close to potential employment?
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The worrying word here is 'potential'. You make it sound like you are unemployed, and you are thinking of moving to Bangkok with the hope of landing yourself a job.
As a foreigner in Thailand, getting a legal job is very difficult. If you have never lived in Thailand before, your chances of getting a job are very slim indeed.
Do NOT consider working illegally or 'under the radar'. Some people do this, and every now and then some of them are caught, fined, imprisoned and later deported with their name on a blacklist. Also be careful about what type of visa you get - you can not work on a 'visa-exempt entry' or a tourist visa. Even if you were able to find employment with a company that will get you a work permit, you would need to leave the country and get a 'proper' business visa first.
Never overstay your permitted length of stay - that can now lead to being imprisoned, deported and blacklisted, if you overstay more than a few months.
The traditional 'easy' job for a foreigner to do in Thailand was that of teaching English. Unfortunately, there have been enough incidents over the years, that now in order to get a work permit as an English teacher you mush have a university degree. And while many schools would be more than happy to employ you without getting you the work permit, see the above statement about illegal employment (i.e. don't do it).
Bangkok used to be an inexpensive place to live. Those days are long gone. Bangkok is now an expensive city to live in, unless you live out in the middle of nowhere. Having said that, if you are looking for a place to live with good connections to most of the city centre, your best bet is next to the BTS or MRT systems, or maybe the Airport Link.
Anyway, to reiterate what I said above - if you are hoping to come to Bangkok and find a job straight away, be aware that it is really not as easy as it sounds.