Count former cities as a source for mining
Whatever did not instantly vaporize upon being hit by a nuke would be radioactive but will still be metal or oxide available for the taking. While "mining waste" would be a lot more durable than most minerals, as it'll be concrete which is pretty much solid stone, the steel under that concrete would not deteriorate enough to not justify breaking that stone up in order to dig the metal. And the metal would still best get smelted into new form than used as is.
Currently, metal in a skyscraper varies in form from thick supporting rails or columns to relatively thin wall filler wires (if bounded cement flowing is used in the process of building that particular house, the wires are about 10mm thick while the main carcass is 25-40mm thick, both types are expected to remain largely intact after being in a wreck state over 120 years), allowing relatively easy transportation after being cut into transportable chunks, and acetylene welding (which can also be used for cutting) and airpump hammers for separating concrete off steel are techs available to the proposed scavengers. Therefore, if the scavengers would find a piece of reinforced concrete, they will be able to retrieve almost all of the metal hidden within.
The amount of metal would be modest
A single house made of reinforced concrete is estimated to contain about 3-10 tons (depending on exact construction) of steel per 100 m^2 per floor, plus extra per main frame which might be absent in case of it being not too high. A skyscraper is an unique building most of the time, most of them have a very hard central core worth about 100 tons of steel per floor (together with literal floors), a city the size of New York would then have thousands of houses 2-30 floors tall and about two hundred skyscrapers remaining after a nuke (give or take a half). Since for mining steel we don't need them standing, but would be happy to find them already fallen, to lessen the risk of cave-in, we count all houses that didn't turn into vapor as available for mining. New York itself is said to be unavailable, but LA is, so assuming 90% of steel-containing houses would remain solid, we might take the current LA as base for calculations.
But, LA looks like being relatively small for the purpose of steel mining. Wiki states it only has 816 buildings of 30 meters tall or above, and 54 skyscrapers (120m or taller) out of them. Wilshire Grand Center wiki page provides some interesting data on its basement's mass - it's said 21600 yd^3 (16500 m^3) of concrete was used to form a 6-yard thick basement, which is solid, totaling to 16500*2400 = 39.6e6 kg or about 40000 tons (only concrete). Elsewhere Wiki states that cross section of reinforced concrete (vertical only tho) contains 1% to 6% steel, since steel density is about 7800 kg/m^3 or triple the concrete density, the mass of steel in reinforced concrete varies from 3% to 18%, thus only that basement is expected to contain up to 7200 tons of steel. However we might not assume that all the concrete used in either the Wilshire or all LA is that rich, taking the more average value of 3% volume or 9% mass would be better estimation for this source's metal richness.
The Wilshire's roof height is 283 meters and it has 73 floors, meaning 73 layers of full concrete over the basement, each no less than 15 cm thick, and its core should account for at least the same amount of mass, and by its basement each floor is 3600 yd^2 (3010 m^2) wide (technically less as the building is not brick-shaped, but we don't use the exact data for the core's volume so this should come close to being evened out if we use lower estimate for core and higher one for floors), so the volume of reinforced concrete in the Wilshire is about 2*3010*0.15*73 = 65900 m^3, so there is about 65900*0.03*7800 = 15.4e6 kg or 15400 tons of steel in the main structure of the skyscraper. This totals to the Wilshire alone having 15400 tons of metal above ground and 7200 tons below ground.
Now, for the other 53 skyscrapers of LA - digging hard for their construction data doesn't seem to be needed, but a skyscraper has to have a modest ground area, otherwise it's a needle and is susceptible to earthquakes which should not be the case for LA's buildings. Thus we can assume that each of them has at least half the ground area of the Wilshire, and since only 19 are below 500ft, we might safely assume that each of them has mass at least a quarter of the Wilshire's, giving their total steel content of 53\0.25*22600 = 299450 tons of steel. High-rises might estimate to each have a tenth of an average skyscraper's worth of steel, or 2.5% of the Wilshire, totaling to 22600*0.025*(816-54) = 430000 tons. Overall, the high-rises of LA currently contain about 752000 tons of steel, this number can be used to estimate how long should the scavengers bother with LA's remains until exhaustion.
(Also note that broken concrete makes good gravel, and there would be some 22 million tons of bravel as steel mining byproduct, to be probably used in new buildings or roads.)
PS: this SO answer states that the total weight of all buildings in Manhattan is 125 million tons. If 9% of that is steel, then Manhattan, even bombed heavily, would still be a better mining site yield wise. Yet I expect your scavengers would not be able to mill over even the LA, due to overall lack of energy to break concrete in the process.