When I was a kid, there was a Japanese restaurant in Boston that
offered a fun meal. You got a dozen bite-sized pieces of raw meat
and/or fish along with a hot rock; and you cooked the food yourself,
on the rock, at your table.

I'd like to know what this dish is called. I'll throw in a tip if you
can refer me to a restaurant that serves it in Boston.

The "hot rock" type of grilling is called "ishiyaki" or "ishi-yaki."

"An ishi-yaki (traditional Japanese stone grill) is used to prepare
delicious entrees..."

In New York: Restaurants
http://www.in-newyorkmag.com/restaurants/alpha/A1.htm

"Ishiyaki - Where a hot stone is used instead of a griddle and
charcoal barbecuing technique. The meats are sometimes dipped in
butter first, which is known as batayaki."

What's Cooking America: Glossary
http://whatscookingamerica.net/Glossary/T.htm

"When fishermen go to catch a fish or shellfish by diving into sea, it
was a custom to provide a stove in the boat. At noon, they boiled fish
and shellfish in a wooden bucket heated with hot stones from the
stove. On shore, where wooden buckets or pans were not provided, they
cooked in a hollow of a rock. This cooking is also called 'ishi-yaki,'
baked with hot stones. The original ishi-yaki was said to be the
cooking of freshwater fish at the bank of a mountain river. In Akita,
this cooking was thought to be very ancient. Instead of using hot
stones, a big rock with a hollow was also used. At first, a fire was
build in the hollow, then food was cooked in the hot hollow."

Media-Akita: Ishiyaki, Isoyaki, Iso Nabe
http://www.media-akita.or.jp/akita-shoku/ishiyakiE.html

"Kato's Midwest Ishi Yaki, a cook-it-yourself affair involving hot
rocks and strips of sirloin."

Evite:  Ohba 
http://www.evite.com/pages/venue/venueDetails.jsp?venueID=KXICPHNLCXVUHGUUPSRF

"ISHIYAKI -
Famous Japanese Style Hot Stone Cooked Steak at your table. Fresh and
juicy beef cooked to your satisfaction with teriyaki or house special
sauce. Try this unique way of cooking."

Kaname Japanese Restaurant: Dinner Menu 
http://www.kanamenj.com/dinner.html#Ishiyaki

There are restaurants in Plymouth and in Quincy that offer steak ishiyaki:

"Sushi Joy
 148 Samoset St. (Rte. 44),
 Plymouth MA
 508-732-9288

Plymouth's first Japanese restaurant features a serene, minimalist
decor, and an extensive menu. Best bets are the ebiten, feather-light,
tempura battered shrimp and vegetables, and the prime sirloin steak
ishiyaki, cooked and served sizzling on a hot stone. Scads of sushi
choices, 21 appetizers, and wine and beer round out the menu."

Boston.com: Restaurants
http://www.boston.com/dining/restaurant/1521

"Name: Fuji Restaurant 
 Address: 698 Hancock Street, Quincy, MA 02170 
 Phone: (617) 773-0888 
 Opened: Mon-Thu: 11.30am - 3pm, 4.30pm - 10pm
 Fri,Sat: 11.30am - 3pm, 4.30pm - 11pm
 Sun: 4.30pm - 10pm 
Reviews: The fish is very fresh and the sushi rice is good. Tempura is
the best in Boston. Sirloin steak Ishiyaki tastes wonderful. The best
steak you can ever taste."

The Sushi World Guide: Fuji Restaurant 
http://www.sushi.infogate.de/rest/na_usa_massachusetts_quincy.htm

I have no doubt that there are other Japanese restaurants in the
Boston area that serve ishiyaki; the problem is that many restaurants
do not list their menu items online. A friend of mine who used to live
in Boston has told me that a restaurant called Ginza used to serve
several ishiyaki dishes. I haven't been able to verify this, but you
might want to check it out.

Some info about Ginza:

DineSite: Ginza - Boston, MA
http://dinesite.com/info/rstrnt-76887/

I hope this is helpful! If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

Another five-star answer from PinkFreud -- who, in my opinion,
deserves a profile in Wired and a nomination for "Best of the Web."
Thank you!

Thank you very much for the five stars and the generous tip, and most
especially for the kind words.

~Pink