Why didn't the Achaemenid Persian armies use the Constantinople area of modern Turkey instead of the Dardanelles to cross to Europe in 480 or 490 BC when invading? It seems like a much easier crossing looking at maps..

You pose a reasonable, if ultimately unanswerable, question here. (I am going to skip past Darius' campaign of 480 that ended at Marathon because that was a naval expedition that did not cross the Bosporus.) Xerxes' expedition was not the first Persian campaign into Europe and Herodotus reports that when Darius launched his campaign against the Scythians (the date is disputed, perhaps 514/513 BCE), his forces bridged the Hellespont near Chalcedon (4.85), precisely in the area you are talking about.

The Persians had also maintained a presence in the Balkans in the intervening years, so the strategic planners of Xerxes' invasion a generation would have been aware that they could build a bridge further north. So why not do that? For one, the location they chose may have been equally, if not better suited for staging and then crossing with a larger army (remember that the invasion of 480 was significantly larger than those that came before). Herodotus specifically says that one of the attractive features of this spot was a broad headland on the European side where they chose to cross. Further, it may be that they chose to take the shortest route all things being equal, perhaps with an eye toward the logistical challenge of keeping the army supplied. When Darius took his expedition to Europe he was taking his army north into Scythia, so his bridge crossed in the north. On his return trip, Darius marched his army to the Chersonese near Sestus (i.e. near this same headland) and crossed with his ships (Herodotus 4.143). Similarly, when Alexander the Great crossed directly into the Troad en route to his invasion of Persia, he likewise used this area on the Chersonese rather than going further north (Arrian 1.11, Diodorus Siculus 17.17, cf. Donald Engels, Alexander the Great and the Logistics of the Macedonian Army).

In sum, we are not given much to work with about why they chose to cross at a particular spot. We don't know, for instance, how much the different currents through the Dardanelles contributed to the decision (maybe) or whether Xerxes was concerned about possible opposition from the Byzantines (probably not, but possible), but if the location further to the north was enough easier to justify going further out of the way then they likely would have done so since they had made crossings at both locations already in the past.