Finally found it, the perfect one..
I had no idea that it would be such a mission to find an apartment that I liked, within my budget, and that would accept foreigners. In the end we were knocked back on three applications because of where we were born, it sucked to say the least. Months of searching webpages, corresponding with agents, and going out to view apartments on freezing cold nights after work does not make for a fun winter, but we were finally successful. Turns out that the landlord of this apartment actually PREFERS foreigners to japanese nationals, go figure.. In any case, we got a great place with tons of space and an OVEN, a rarity here in good old T-town..