An ICBM (which is what you're usually talking about with nuclear bombs) takes about 30 minutes to reach its destination, which will be a large population centre.
So, you have less than 30 minutes to get out of a large city. Because you won't be the only one to try this there will be major congestion on top of the usual city traffic. Public transport could be an option but I wouldn't be so sure that trains keep running either once such an alert has been issued.
The total destruction radius of current ICBM warheads is much smaller than large population centres - if you live in one, and a single 2-5 megaton nuke would hit it, you likely won't die even if you stayed where you are (but duck&cover'ed, preferably in a basement, to avoid the secondary effects) because that nuke would hit some other district of your city; for any major population center the expected casualties from a single hit are just a small portion of the total population.
An ICBM (which is what you're usually talking about with nuclear bombs) takes about 30 minutes to reach its destination, which will be a large population centre.
So, you have less than 30 minutes to get out of a large city. Because you won't be the only one to try this there will be major congestion on top of the usual city traffic. Public transport could be an option but I wouldn't be so sure that trains keep running either once such an alert has been issued.