Tsunahachi has been frying prawns and veggies for more than 90 years and is an easy place to be initiated in the art of tempura. Come at lunch for the inexpensive hiruzen (昼膳; ¥1510) lunch special; it's advertised out front but not on the English menu inside, so ask for it by name. Indigo noren (curtains) mark the entrance.
Tsunahachi has several outlets around the city, often in department stores, and is always a safe bet. This is the main shop.