Welcome to Gaia! ::

In such an event, you need to look at where you are geographically before making a move. The best idea is to head into the sewers, pretty much anywhere underground to avoid nuclear wind will do, but the sewers will allow you a very wide network of travel. You will be one of only a few survivors, but that doesn't mean you should be wasteful with your supplies. I hate to say it, but your main source of drink will be rat milk, and your main source of food will be, yup, you guessed it, rat. It's best to keep the females apart from the males until you need to breed them to keep your supply up, separate cages for each rat are best, but where will you find that. When selecting a rat for food, go for the males, they are generally larger and don't produce milk. Just don't go overboard.

Well, that's why I say sewers, a very broad network of travel, plus, it's not really to completely avoid it, that's impossible, it's to have a safer radiation level and avoid the nuclear winds.
P.S., welcome to the guild, from the get go, I can tell that you will have useful input here, that's what I'm looking for in members.

Nuclear chemicals travel airborne for a very long time. The sewers are not sealed air-tight. If they were, you wouldn't be able to get oxygen, at least not enough to overpower the stench that would partially suffocate you. In other words, the chemicals in the air would seep into the sewers very quickly and clog them, not to mention accessing the sewers through water and waste. It would be a death trap without any resources to survive on. Radiation would be at potentially higher levels there than even ground zero.

Nobody within the radius of the attack could possibly survive a nuclear holocaust within a properly made bomb shelter. It just isn't realistic.

What about vaults? It sure worked in fallout....