It's a bit late for lunch now, so the prices will be considerably more than 1,800yen but Pickles made the following recommendation a couple of months ago:

Morita-ya, in the 35th floor of the Marubiru (Marunuochi building 2-4-1 Chiyoda Ku). Old-style Kyoto beef restaurant. 200g steak, soup, rice, salad, pickles, for 1800 yen (lunch time only!)

Tel: 03-5220-0029
http://www.moritaya-net.com
Maps with how to get there: http://www.marubiru.jp/05_access/access.html

I think the evening meals start at 5,250yen.

Special selection sukiyaki course

* Japanese Cattle sashimi or Japanese Cattle hitting
* Meat cooking 150g
* Vegetable
* Boiled rice * red miso soup * capital pickle or noodles * red miso soup
* Fruit
11,550 Yen

Pine sukiyaki course
* Meat cooking 150g
* Vegetable
* Boiled rice * red miso soup * capital pickle or noodles * red miso soup
* Fruit
8,400 Yen

Bamboo sukiyaki course
as above (Pine)
6,820 Yen

Plum sukiyaki course
as above (Pine)
5,250 Yen

I think they have steak too from 7,870Yen:

The Kyoto meat special selection stake course
250 g Roast 13,120 Yen (Fin 14,430 Yen)
Japanese Cattle sashimi OR Japanese Cattle hitting and meat cooking, vegetable salad,
Boiled rice * capital pickle, red miso soup and coffee * dessert

200 g Roast 10,500 Yen (Fin 11,550 Yen)
Japanese Cattle sashimi OR Japanese Cattle hitting and meat cooking, vegetable salad,
Boiled rice * capital pickle, red miso soup and coffee * dessert

180 g Roast 9,450 Yen (Fin 10,390 Yen)
Japanese Cattle sashimi OR Japanese Cattle hitting and meat cooking, vegetable salad,
Boiled rice * capital pickle, red miso soup and coffee * dessert

150 g Roast 7,870 Yen (Fin 8,660 Yen)
Japanese Cattle sashimi OR Japanese Cattle hitting and meat cooking, vegetable salad,
Boiled rice * capital pickle, red miso soup and coffee * dessert