I will be travelling to Miami on Monday 6 June and will be on the
ground for about 6 hours (3 hours after airport procedures). I am not
a US Citizen or Resident and do not have any US bank accounts. I am a
gold AMEX card holder and have a Citibank Australian Account if that
helps. I need to deposit about US$7000 in a Miami Bank and was taking
cash with me to deposit with this bank. I have now discovered that
they are a "commercial bank" (or similiar?) and do not accept cash
deposits. That is, they need a check or a funds transfer.

My Questions: Is there a bank or other reputable financial institution
where I can pay cash to obtain a check (bank check) for a reasonable
fee. This locale would have to be reasonably close to the airport
(Downtown is acceptable) and I would have to be able to complete this
within a couple of hours. It would also be bonus if I could purchase
AMEX travellers cheques at the same locale.

Hi, 
Since you have an Amexco card, that would be your best reference. 
Coming to the States with a lot of US dollars may not look so good.
This site gives American Express offices in the area, some with phone numbers.
I would suggest that you try to contact them before you arrive, to
find the one nearest the airport and whether they will sell you
travelers checks against cash dollars, or let you deposit them as a
credit balance to your card account.
They might want to make either transaction subject to being able to
charge your account for possible counterfeit notes (just my cautious
ex-banker's idea).
Maybe your local Amex office can help you with advice.
Or maybe you have to fly on to your ultimate destination first, an
easier solution than the risk of missing your onward flight.  Airport
security controls can be time consuming.

http://ypng.infospace.com/_1_KNPUCP021SZOYG__info.adrses/ypv3/list.htm?&kcfg=ypus&ypinsp=0&searchtype=all&qhqn=American+Express&qn=American+Express&qc=miami&qs=FL&qk=15&xmlurl=http%3A%2F%2Fapi.superpages.com%2Fxml%2Fsearch%3FSRC%3DInfospace%26search%3DFind%2BIt%26PG%3DL%26CS%3DL%26T%3Dmiami%26PB%3D%26S%3DFL%26Z%3D%26A%3D%26X%3D%26P%3D%26CID%3D%26K%3D%26C%3D%26N%3DAmerican%252BExpress%26PI%3D%26NA%
3D%26STYPE%3D%26R%3DN&qsubcat=firstpage&ypfwd=1&24105

This is the site that gave me the above:

http://miami.travelers-checks.addresses.com/s1/166.html

This is from the site below:

"Money
There is no limit on the total amount of monetary instruments that may
be brought into or taken out of the United States, nor is it illegal
to do so. However, if you transport or cause to be transported
(including by mail or other means), more than $10,000 in monetary
instruments on any occasion into or out of the United States, or if
you receive more than that amount, you must file a report (Customs
Form 4790) with U.S. Customs. Failure to comply can result in civil
and criminal penalties, including seizure of the currency or monetary
instruments. Monetary instruments include U.S. or foreign coin,
currency, travelers checks, money orders, and negotiable instruments
or investment securities in bearer form."

http://www.foreignborn.com/visas_imm/entering_us/3customsinfo-nonres.htm

Have a good trip, Myoarin