I finally had a chance to try out the vegetable kaiseki at Nagamine in Ginza, and it was very impressive. The restaurant is a few years old, and it's run by a 60-year-old vegetable wholesale company based in Tsukiji. The Y5250 vegetable kaiseki seems designed to showcase their top-quality vegetables, and it changes every month. (They also have kaiseki menus for Y8,000 - vegetables plus fish - and Y12,000 - vegetables plus meat.)
The December menu was seven courses in the usual kaiseki structure (http://r.gnavi.co.jp/b803900/menu1.htm ), starting with a glass of very sweet tomato juice, a vinegared vegetable dish served in a hollowed-out yuzu, and a tofu-like sweet-potato-based dish. Everything was beautifully arranged, with a red-orange-purple color theme running through the entire meal, including a vividly colored thick soup made from red turnips, which was one of the highlights. Another high point was the beautiful vegetable sushi platter, which seems to be their signature dish. And the dessert of cauliflower cream-cheese mousse with brandied raisins was sublime.
They have a small but unusual sake selection, including a Y1200 three-part tasting set, with the selection changing every month. The interior is tasteful, and they seem to have a lot of private rooms, including for parties of two. We made reservations late and sat at the counter, which is used more as a prep station with staff wandering in and out to heat sake, etc.
Service was poor for the price level - the staff explained each dish for the first three courses, then stopped bothering, and it took a major effort to attract their attention to get water refills, order more sake, etc. Each glass of water was served with a beautifully carved globe of ice just like in a fancy bar, but I would have preferred a simple refill from a pitcher.
In spite of the service, I think it might be a fun experience for visitors who want to see an unusual take on kaiseki at a very reasonable price. Every dish was outstanding, a few were quite memorable, and the presentation was simple but attractive. They have an English web page, so I assume they're ready for non-Japanese-speaking customers. (There are no menu options for strict vegetarians though.)