Breakfast on Kauai?
This place looks like a real hole in the wall, but their breakfast is GREAT, especially the Macadamia nut pancakes (with coconut syrup). Its on the first floor of the Tip Top Motel, which also looks like a hole in the wall. Give it a try - you won't be diappointed, but be prepared to wait.
Tip Top Motel Cafe & Bakery
3173 Akahi St, Lihue, HI 96766
Tip Top is in Lihue, not in Poipu so you could need to drive 20-30 mins to get there.
The only affordable breakfast option in Poipu at this time is Joe's on the Green. If you have jetlag and get there early (I think before 8??) the prices are really cheap. It is located in the Poipu Shopping Village, near Keoki's or Puka Dogs.
If you got a little bit further out, there is Kalaheo Cafe in Kalaheo (more west than Poipu), which is very popular. Personally I don't like it, but I am in the minority. In Lihue you can go to Tip Top or Dani's. Both very small, very local places.