Unfortunately, not all countries work that way. China happens to be one of them. (To be fair, these policies -- and the accompanying fees -- tend to be reciprocal between countries.) With B. about to hit the 30-day limit on his visa, we decamped to Hong Kong.
Fun fact: China and Hong Kong currently work on a "one country, two systems" system. Americans need to obtain a visa before visiting China, showing flights in and out of the country and a hotel reservation. There's no visa required for Hong Kong, though. Going to Hong Kong counts as "leaving China" from a visa perspective, so it's a common destination for travelers looking to reset the clock on their stay in China.
With apologies to my Hong Kong friends, I haven't been a huge fan of the country. For a few years, B. resided there, living in Jordan and working in Central. When I visited him, those were the parts of Hong Kong that I saw. Everything in Central is finance-related or shopping-related, and it's all teeming with people. The urban area of Hong Kong has one of the highest population densities in the world.
The view from B.'s old Hong Kong apartment.
Densely crowded places + excessive amounts of shopping is not a recipe for a happy Sarah.
After this this trip, however, I'll say that I may have judged Hong Kong too quickly.
This time, we stayed in Sai Kung, 35 km (22 miles) and a world away from Central. Sai Kung is a former fishing town; it's too big to be called a "town" anymore, but it's practically unpopulated compared to Central and it hasn't strayed far from its fishing roots. We took a boat ride around the harbor, ogled the selection at the seafood restaurants along the water -- which would rival many reputable aquaria -- and picked out new and exciting foods to try. We stayed just long enough to buy tickets for our next destination: Thailand.