How long after signing a settlement agreement with the city should I receive my check?

Generally, within 30 days.

About a month. The paperwork needs to be processed in the respective departments.

It should be within 30 days, but in reality it will probably be 60 to 90 days.

Unless the Settlement Agreement gave a specific time for performance, there usually is no set time. With governmental agencies it can depend on whether approval of the settlement by the "powers that be" (i.e: City Council, City Manager or whomever is required to give approval in the particular City) was given before the settlement or has to be gained after the settlement. Typically the settlement process with a City can take longer than with a non-governmental defendant. But it can also depend on whether they were covered by insurance for your claim or it comes out of their general fund, with insurance paid claims usually coming faster due to less "red tape" in the process of settling and paying the claim. The law will usually impose a "reasonable time" requirement, so if you don't get your $ within 2-4 weeks, you could have your attorney file a Motion with the Court to ask for an Order to Compel the payment in "x" days (of course, filing the Motion and waiting for a hearing date add days/weeks to the process).