I did something similar to a dead city that had to be fled in a fairly hasty way because there was a chaos taint that was spreading throughout the city. Here was my step-by-step process for looting the city:
1. Take your city and divide up it by sections like placing it on a hex grid or something. This determines the maximum number of areas for the PC's to go around stuffing their pockets.
2. For each section of the city determine the maximum amount of wealth the PC's will be able to collect should they literally search door-to-door. For example, if you have a slum area, the PC's will find 150 gp, but if they go into a noble's area, they can find 1,500 gp
3. Define the types of actions the PC's can do in each hex and specify the amount of time it will take. Here's what I did:
a. Travel. The PC's just move and explore through this hex just to get somewhere else. Roll for % for a random encounter, but they collect no gold. Moving through this district takes minimal time. If there is a planned encounter here, it is automatically triggered
b. Hastily Explore. The PC's pick the most interesting places in the hex and give them a look through. They will only manage to find 20% of the max gold in this hex and automatically run into the planned encounter with a normal chance for a random encounter on top of it. The time spent in this hex is dependent upon how much area there is to cover, but I had a small city so this was eight hours of exploration. If you have a large city, you'll want to increase that time.
c. Thoroughly Explore. The essentially "take 20" on the hex. They will yield the maximum gold to be found for this hex. They will automatically trigger the planned encounter and roll for random encounter for each day spent. Now I didn't do the 20 times the Hastily Explore option (I did three times), but you're well within your right to have the PC's spend 20 times (or less or longer) if they want to ransack every hut, building, and stall in the hex. They will also bring a lot of attention to themselves as they are constantly spending time in a ruined city.
4. Develop planned encounters for certain areas. As part of the risk/reward for exploring and looting, have certain areas of your city with planned encounters. These are monsters or hazards that the PC's have to overcome for trying to earn "free gold".
5. Develop random encounter tables for monsters/situations and extra treasure. As the PC's explore each hex or section, they run the risk of triggering a random encounter, but these encounters could be monsters, friendly or injured NPC's, or other situations. Also, in addition to the potential max gold, you can roll for a random treasure too. How much of extra mundane / magic items of stuff is up to you.
A couple of notes though:
The first is that most of the gold yield is cash. If the PC's are also looting for mundane stuff like armor and weapons, then it's up to you to determine how much of that is also around as well. For me, I had placed it at three times the maximum gold yield; however, I wanted the PC's to show me how they were going to carry it and secure it, because if they couldn't manage to do both, it would be stolen or gone.
The second is that if the PC's are spending a lot of time in a ruined city, then they need to figure out how they are handling issues of food and water. Exploring a city takes considerable amount of time so food, shelter, and water are fairly important.
The last is assessing risk with reward. If you have a mundane city, then the gp yield should be fairly low with low-level encounters and probably not worth the time if your PC's are high level. However, if this city has a reputation of being a place of great power, fierce evil denizens, terrible magics, then the cash yield and monster placement should be higher. For example, in the Forgotten Realms setting, Myth Drannor was a tough place for mid-level adventures and Narfell was a challenge for higher level adventures.
Have fun!