I used to work on Wall street a few years ago which is right next to Broad street. That area is the financial capital of NYC, you may find studio apartments there but expect to pay a lot of $$$$$ and the area isn't conducive to residents (most delis and restaurants close on weekends and are closed by 6 or 7 pm weekdays). Your best bet is the area around Battery Park city, this has many residential buildings, a movie theater, and some small markets for the locals..it's about a 20 min walk to Broad Street (maybe more or less depending on specific route or street you use). Another option is the area near South Street Seaport but I think there were mostly low income housing there (from what I remember when I searched for housing near Wall St).
There are 1 or 2 residential buildings right ON Wall St but like I said, they are super expensive and if you plan to go grocery shopping on weekends, you would have to take the subway uptown. By expensive I mean, monthly rent is easily $2500-3,000 and up for a studio.
As far as business attire, I would dress conservatively, but the dress code will vary depending on your company. At my old firm, the IT guys would wear polo shirts and khaki pants. You want to look neat but not "too" casual (ie jeans and sneakers not recommended). Of course, if your employer is a small organization with only 10 Employees, you may be able to wear jeans.
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