I found that purchasing the "Prepared Traveler" LTR really helped me to make it to Visa level 3 quickly because even the very first time I went to any of the locations, I was able to stay 6 days instead of 3.
Another thing that helps, though it IS kinda cheating, is to use the teleport option frequently instead of wasting so much time running back and forth to locations. I don't like using the cheats at all when I'm exploring, but the travel time between locations is ridiculous! Especially if you take something to somebody and they tell you, "Oh I forgot to mention that I need this too" and off you go again for another 3 or 4 hour trek across the country to get the forgotten item. When I first got WA, I never used ANY of the cheats and I did eventually get to visa level 3, but it would often take 3 or 4 trips there to get it just because of all the wasted running time.
Also, once you get enough gold coins, my favorite things to buy from the Special Merchant are the "Tear of Horus" in Egypt and the partnership certificate with all the countries to allow you extra time in country.