Of all the jap places I've been to in Singapore, I think that Beppu Menkan Jap restaurant has the best and most value for money eel on rice. A friend took me to this place about 2 years ago and since then I've been introducing all my friends to this place. Everyone knows that eel (unagi) is relatively more expensive as compared to other dishes however at Beppu, it only cost $10 for a bowl of eel on rice and miso soup! Shiokness.
So far the only outlet I've been to is the one at Tiong Bahru. Can't remember which floor it is on but it's opposite or next to Sakae Sushi.
You can sit inside or outside. This place is extremely crowded during peak hours and it's rather romantic to sit outside at night cos the weather would be quite cool (they also provide fans) and I like the candles :p

Eel on rice! Price: $10
As you can see, they give heaps of rice and the eel is heavenly. $10 is really worth your money as compared to a lot of other places such as Ajisen Ramen. Ajisen has the exact same thing for $13.90 or $14.90 (can't rmb) and I dunno if the portions are even as good. A must try!