Fair point about the personal drama. There is some engagement with economy, tax and the likes, but it doesn't really add up, which is fair enough. To write about something realistically you have to know your stuff, and at the end of the day he's not an economist or historian specialising in the affairs of the realm. Neither are most of his audience as well, so it's alright.
As far as I'm aware it seems to be quite a maritime economy, considering the rivers and trade with the Free Cities.
The Reach is rich in wheat and other foodstuffs, ships up the Mander. Has the highest population of the regions. The Arbor produces luxury wine. Oldtown is the biggest city in Westeros and has a near monopoly on the trade of scholarship.
Dorne's population is centralised on the Greenblood river and the west coast. It seems to ship off luxuries, oranges, lemons and Dornish gold wine.
I know little about the Stormlands. It's a fairly mountainous and desolate region with lots of storms. No major cities.
The Riverlands has lots of small towns such as Harroway's and Saltpans. A lot of trade presumably happens over the rivers, and it's a fairly fertile region.
The Westerlands are hilly with lots of gold mines. Lannisport is their principal city.Among the hills it seems fairly fertile.
The Vale is very mountainous with the fertile Vale of Arryn in its centre. The edges are all windblown. Gulltown is its largest city.
The North is the largest region, and sparsely populated. I guess it has a strong lumber trade from the large woods. White Harbour, its main city, is on the mouth of a river, situated to receive goods from further inland.
Fuck all is exported from the Iron Islands.
Tyrion puts a tax on brothels during ACOK which makes him unpopular. There's other examples, but I can't remember exactly.