1234,"Calle Jaime III, 34", 67,3,U
1235,Avenida Los Algodones, 12,1,L
1236,"Calle Principal""31234", 46,3,H
1237,"Calle Alfonso X,22", 65,2,J

1234    Calle Jaime III 34       67     3     U
1235    Avenida Los Algodones    12     1     L
1236    Calle Principal 31234    46     3     H
1237    Calle Alfonso X 22       65     2     J

,(?=(?:[^"]*"[^"]*")*[^"]*$)

String line = "1234,"Calle Jaime III, 34", 67,3,U";
String[] tokens = line.split(",(?=(?:[^"]*"[^"]*")*[^"]*$)", -1);
for(String t : tokens) {
    System.out.println("> "+t);
}

String line = "1234,"Calle Jaime III, 34", 67,3,U";
String[] tokens = line.split(",(?=(?:[^"]*"[^"]*")*[^"]*$)", -1);
for(String t : tokens) {
    t = t.replace(",","");
    t = t.replace(""", "");
    System.out.println("> "+t);
}