I'm talking about language, culture, architecture, art, etc. Anything that might make it apparent today (even to non-historians or non-archaeologists) that they once controlled the territory.
The question also applies to other Germanic peoples that settled in Iberia prior to the Visigoths (I only know about the Vandals and Suebi).
The answer most certainly isn't, "none," it's just that their heritage isn't easy to notice.
In 409 AD two groups of Vandals, the Asdingi and Silingi, a group of Alans under Respendial, and the Suebi crossed the Pyrenees and started dividing up the Iberian peninsula. The Romans, once competent leadership under Constantius III had raised morale and mobilized the Italian field army, first addressed the situation in Gaul and then in turn defeated these groups in Spain, giving them official terms of "settlement" and "federation." However, unlike the Visigoths, Burgundians, and Franks, we have no idea what these terms were, although we can guess at them.
Barbarian migration and settlement did not happen like most people believe. Massive numbers of germanic-speaking peoples did not pour into the Roman empire, slaughtering Romans in their wake and defeating armies and burning cities. These groups were mostly the upper class and the warrior populations. When peoples were displaced, the average man was simply content with whomever the new guy ruling over them was. He didn't have the food, resources, and money to migrate with his family. As a result, the incoming migrants groups were small in size, and were basically armies with baggage trains of their families. These groups primarily did not number more than about 20,000 men. As a result, they ended up having only a small impact on the population where they were settled, being outnumbered by literally millions of Romans.
The other issue is that of the actual nature of settlement. Barbarian settlement wasn't actually the presentation of land to these migrant groups, at least not in the time period we're discussing (382-443 AD). It was basically the allocation of tax revenue from local lands to directly pay them for military service and civil administration. Sometimes they would receive land from agri deserti (deserted farmlands) but this wasn't usually standard. It's believed that what ended up happening is that they took the treaty terms and law that said allocation of 1/3 tax revenue from allotments and turned it into 1/3 allotments of land, but this requisition of land from local aristocrats wasn't permitted until later treaties in the 440's or 450's (at least according to Guy Halsall's argument.) Dispute over tax allocation versus land allocation may be one of the reasons why the Battle of the Catalaunian Fields is used as a deliminating year in Burgundian Law, in fact.
So, these peoples in Spain were not settled on farmlands, at least not initially. They had nowhere of their own to build churches or other macroscopic cultural artefacts because they didn't own the land, and anything macroscopic they did do could not be performed without interaction and utilization of the Roman population, Roman culture, and the local late Roman administrative system. Meaning that anything they did do would have been difficult to distinguish from the local Roman styles, due to the heavy cross-cultural interaction.
And that's why what evidence we do have of them is difficult to differentiate. It comes mostly in the form of minutiae like cloak brooches, belt buckles, etc. Bienvienida-type belt fittings, for example, which have Germanic influences but were used just as much by the local Romans as they were the Germanics. Structures that were built in this period are indistinguishable in determining whether they were Roman or Germanic sponsorship, or art styles. Both sides heavily influenced each other.
They did leave a legacy, but that legacy was drowned out by early 5th century Roman, and then Visigothic assimilation. By the time the Goths moved into Spain in the 460's, the old techniques of settlement and assimilation had broken down, allowing them to have a much greater cultural impact. This is on top of the fact that much of the Vandal/Alan/Sueb stay in Spain was either brief or heavily contested, as the Romans were still militarily potent and capable of submitting them to their authority under Aetius, while the Vandals and Alans emigrated out of Spain and left a much larger cultural impact in North Africa.
Sources:
Goffart, Walter. Barbarians and Romans, AD 418-584: The Techniques of Accomodation. Princeton: Princeton University Press, 1980.
Fernandez, Joaquin. "Late Roman Belts in Hispania." In Journal of Roman Military Equipment Studies 10 (1990): 55-62.
Kulikowski, Michael. The End of Roman Spain. Toronto: University of Toronto Press, 1997.
Livermore, Harold. The Twilight of the Goths: The Rise and Fall of the Kingdom of Toledo c. 565-711. Bristol: Intellect Books, 2006.