Onsens for those who can’t speak Japanese?

So I arrived at Tokyo today and have 5 days left on my trip here. I had planned in advance to spend 1 day at an onsen, probably at the Odaiba onsen. However, I just read somewhere that onsen are designed primarily towards Japanese people, not foreigners like me who can't speak Japanese. Also, I have never worn a yukata before. I am a male, so I am fine with being nude in front of other males. But I am an Asian American, so I feel a little embarrassed to ask others to explain things in English as I know the Japanese are polite, but can be rather xenophobic

Is going to the Odaiba onsen not a good idea for an Asian American like me who can't speak English? Are there other onsens that would be more English-friendly?

No language skills are required for onsen. However, you should be familiar with the onsen customs:
http://www.japan-guide.com/e/e2292_how.html

Oedo Onsen is particularly foreigner-friendly with lots of bilingual signs.

Also, I have never worn a yukata before.

How to wear one:
http://www.japan-guide.com/e/e2029_dress.html

And try to get rid off of your impression that the Japanese are xenophobic. Such prejudices are utterly useless and may reflect negatively on you.

Language barriers should not be an issue. A large number of Japanese tourists are actually from China and Korea, so they would be used to it.

I just went to an onsen in Kurokawa recently (which is not as popular with foreigners compared to some other areas) with very minimal Japanese and was completely fine :)

The only time you might get into trouble is if you have a tattoo. But other than that there shouldn't be any issues, especially in a place like Odaiba.