Kaiseki ryori is the highest form of Japanese food, and the most expensive. It is creative, delicate, subtle food like no other, and has been the inspiration for the Nouvelle cuisine of France. It is perhaps the only kind of food in the world where you feel it was worth the $150 (without drinks). Generally a meal consists of dish after dish after dish of food you have never seen or heard of before, appearing at just the right pace across an evening. Sake is the best drink to accompany any kaiseki meal, and it's generally dry and served cold. Kyoto probably has the best kaiseki culture in Japan, though many of the best restaurants do not take walk-in customers (you must know the owner), and would set you back upwards of $1000 per person anyway.
Nihon Ryori Kagaman, located in the upscale night scene of KitaShinChi, is one of the best kaiseki restaurants in Osaka, and can make for a truly unforgettable (if expensive at ¥15,000 per person) evening out. The chef takes a daily fast boat to the fish markets of nearby Awaji Island to purchase the best possible ingredients, and makes a policy of minimal preparation to ensure freshness (even soup stock is made at the time the order is received). Lunch is reasonable, where for ¥3,000 you get a choice of a Soba Kaiseki set or a seasonal lunchbox. Ordering is easy (always by course) and is divided by price. Nihon Ryori Kagaman has a counter on the first floor, and it's always interesting to watch the chef prepare the food, though the semi-private tatami rooms upstairs are in many ways nicer. If you are in a party of four or more you may be able to sit on the Japanese-style open-air terrace. Try and get somebody who speaks Japanese (at your hotel maybe?) to call ahead and make reservations.