In 1924, FIFA decided to assume responsibility for the organization of the Olympic Football Tournament. That tournament was won by Uruguay -an underdog at that time- against Switzerland, with an estimated attendance of 60.000 people, an absolute success in popularity. Four years later, with the same conditions, Uruguay won again against Argentina. By that time, the predominance of South America in general and Uruguay in particular was incontestable. That same year, FIFA decided to organize its first FIFA World Cup. Uruguay was the current world champion, a football superpower, and a country with European levels of wealth (being called 'The Switzerland of America'). Besides that, 1930 was the year of the centenary of Uruguayan independence, so it was an obvious choice for them.
While I have no idea of the levels of foreign attendance of the matches of that World Cup, it's true that almost all European teams declined the invitation to the tournament because of transportation problems and/or lack of interest. The final was played in the Estado Centenario (Centenary Stadium) and, again, Uruguay won the world title against Argentina. Twenty years later, Uruguay won another final in MaracanĂ¡ against Brazil. That's why the Uruguayan shirt has four stars instead of two: They reflect their two WC, but also the two official FIFA world championship titles that were played before the first FIFA World Cup.
Sorry for the bad English.
In order to answer the question I'll have to go into the immediate time before the 1930 World Cup. This post will be somewhat lengthy as a result.
By the late 1920s FIFA as an organization was riding high from having helped organizing the previous Olympic football competitions, starting with the 1908 Olympics - and reaching its peak at the 1928 Games in Amsterdam.
Official match reports from the Amsterdam games' first round tell us that attendance ranged from 1 200 people watching Yugoslavia - Portugal to over 27 000 people attending the hosts' 0-2 defeat to Uruguay. Keep in mind that this was the Round of 16 (whos attendance figures generally kept under 10 000).
Interest did swell the closer the tournament came to the final - the quaterfinals averaged 10 500 spectators over 5 games (including a replay of Italy - Spain, the first leg ended 1 - 1, the second 7 - 1 to the Italians), the semifinals 11 500, and the final itself saw 28 000 in both the first game between Uruguay and Argentina as well as the replay. Uruguay won the replay 2 - 1, thus succesfully defending its gold from 1924.
This success - the 1928 Olympic tournament brought in almost a quater million spectators (246699) spurred Jules Rimet - then President of FIFA - to consider striking out of their own. Barbara J Keys notes in her "Globalizing Sport" that while the Games had been lucrative indeed, the attendance numbers also showed a popular demand for the best players and the best teams. The Olympic example also meant that national teams would be vastly preferred over club teams in a World Cup competition.
At this time - while proffesional leagues had begun to spring up in much of Europe and semiproffesionalism likewise in Argentina, Uruguay and Brazil - the growth of proffesionalism within football caused such a severe outcry that the four British nations left FIFA and the IOC threatened to ban football from the Olympic program if stricter rules were not implemented. With the footballing world embrolied in this controversy - a question that would come to affect the first few World Cups* - there were real factors pointing FIFA towards striking out on their own in case the Olympics would no longer be an option. Thus, the World Cup - from its outset - accepted proffesionals. [1]
(Yes, the World Cup was born partly out of profitability and money making concerns. I can hear the snide remarks about FIFA's current and recent state all ready - but that's completely out of the purview of the answer.)
And so FIFA went to work - FIFA made the decision to start up the World Cup in its 1928 Amsterdam Congress - where prospecting hosts could submit their bids - and the decision regarding hosting duties came down to the 1929 Congress in Barcelona. At the 1929 Congress, Dr. Beccar Varela of Argentina argued in Uruguay's favor over Italy, the Netherlands, Sweden and Hungary. The European countries all withdrew their candidacies after Italy was rejected - and Uruguay got the hosting duties unanimously.
Another important factor that ties into Dr. Varela's second point is the stadiums used at the 1930 World cup; all of them in Uruguay's capital Montevideo. The then newly built Estadio Centenario was an absolute giant at 90 000 capacity. Gran Parque Central clocked in at 20 000. And while Estadio Pocitos only took in 1 000 officially - its two games saw 4 444 for the opening game between France and Mexico (where the first ever World Cup goal was scored) and 2 549 for the game between Peru and Romania.
As for why 70 000 people attended the first World Cup Final? Not only were the Uruguayans two time Olympic champions - the first of the four stars on Uruguay's crest per permission from FIFA - but they were immensely popular among the native Uruguayans. Uruguay's two group matches against Peru and Romania saw 57 000 and 70 000 spectators respectively. The game between Peru and Romania saw - as earlier mentioned - "only" 2 500 in attendance at the tiny Pocitos. Likewise, Uruguay's semifinal against Yugoslavia drew in almost 80 000 people to the stands.
That said, Uruguay were not the only ones drawing in sizeable crowds. The average attendance of 32 000 includes the only four games out of the tournament's eightteen which saw sub-10 000 in the stands: the aformentioned Peru - Romania, France - Mexico, Chile - Mexico and Chile - France**. Chile, France and Mexico were Argentina's group opponents; and Argentina themselves drew in between 20 000 and 40 000 for their group games. Argentina's semi final against the United States, played a day before Uruguay's, saw 72 000 spectators.
And with that the stage was set for the final. Both Uruguay and Argentina were clearly very popular teams to attend. Also, not only had they squared off 2 years prior in Amsterdam; both teams had come into the final without a defeat to either their names. Both teams were among the best at the time, and featured prolific goal scorers (Argentina's Stabile and Uruguay's Cea - both of which would net in the Final itself). This is something supported by the footage from the Final compiled by FIFA - notice that the Stadium's absolutely packed for the match.
With those data points, it's actually still rather difficult to answer how many foreigners arrived to see the games. In both the 1928 Olympics and the 1930 World Cup, average attendance reached the 5 digit range quite often. Regardless of if the host nation played or not. It does signal significant interest in the matches.
Also, Clemente A. Lisi's book "A History of the World Cup 1930 - 2014" notes that thousands of Argentine fans made the boat journey to the neighboring Uruguay in an attempt to see the Final, for instance. While I couldn't find any clear data on how many foreigners attended over the whole tournament, both the Olympic Games and the World Cup point towards at least thousands, if not tens of thousands in the World Cup's case. Given that Uruguay tightly connected to both Brazil (Brazil saw around 25 000 spectators in both their games) and Argentina, and that the vast majority of 1930's participants were American, travelling to Montevideo was not an issue for a lot of foreigners from the American continents. In any case, the interest in matches where the Netherlands (in 1928) and Uruguay (in 1930) didn't play in supports the point that people indeed flocked to football games featuring big national teams. Whether the fans came from the hosting country, or abroad.
*For example, the decision by Sweden to bar professional players from their World Cup squads up until 1958.
** Lisi claims that the attendance figures were different - for example that just 800 people saw USA - Paraguay. However, the official FIFA report gives a number of 18 000 in attendance. RSSSF backs up FIFA's number, with a number of around 20 000.
Sources: [1] Keys, Barbara J. "Globalizing Sports - National Rivalry and International Community in the 1930s" 2006 Harvard University Press.
Lisi, Clemente A: "A History of the World Cup: 1930-2014" 2015 Rowman & Littlefield.
FIFA's match reports from both the 1928 Olympics at Amsterdam, and the 1930 FIFA World Cup at Uruguay (Montevideo). With double checking from RSSSF. The numbers do differ between FIFA and RSSSF - RSSSF claims that 80 000 people attended the Final. Nevertheless, both FIFA and RSSSF agree on the general scope of attendance - most 1930 World Cup games drew in 10 000+ at least.