Csikos Hungarian Restaurant, at 3601 Connecticut Ave. NW, in the Broadmoor Apartments, looks pretty sedate, with red draperies, chandeliers and a rather hushed clientele. But no one seemed to find the entrance of children, aged 6 to 9, out of the ordinary.

"Snails? And rabbit?" asked my 9-year-old daughter, after a look at the menu. Finally she decided that you only live once and, at least, she could tell her friends about them the next day.

We started off by splitting some cold cherry soup, at $1, with whole cherries and an order of Hungarian-style snails, $2.75, which came on top of muchroom caps with a very tasty sauce. Both went over well, even though we had stuffed ourselves with the good rye and pumpernickel bread. It was a longish wait; the waiter hadn't mentioned that snails take a while.

For our main courses, we decided on beef goulash at $5.60, rabbit hunters style, $6.25, and a thin pancake stuffed with meat from the appetizer section, $1.95, for the youngest. It was a tough choice. Other alluring possibilities were feal paprikash, $6.30; roast duckling with red cabbage at $6.95, and a combination plate for the curious, $5.50.

"Mmmmm, this is good!" said my daughter as she tasted her rabbit. We all tasted each other's dinner and were generlly pleased with the food, although the goulash could have been more tender. The beef goulash came with parsley potatoes, the rabbit with homemade dumplings. The pancake, stuffed with a ground pork an dbeef mixture, was agreeably spiced.

We wished we had discovered earlier that there were children's portions of the beef goulash and several other things, for the servings are mighty big.

Dessert was an heroic effort, but we made room. My daughter and I chose an elegant mound of chestnut poree with whipped cream and cherry at $1, while my son had chocolate ice cream, 75 cents.

Csikos' strolling violinist of yesteryear is gone, but there are some good items to interest kids when they tire of dipping parsley in their ginger ale. We looked at the lovingly dressed Hungarian dolls, the unexpected side room with Day-Glo decorations and several costumed wine bottles. We also talked to the maitre d', who was happy to show off how he sliced smoked salmon.

Our total bill, including a ginger ale and a Coke, came to $23, but you can reduce that by ordering children's portions.

By the time you've crossed the stately Broadmoor lobby, you may wonder whether a fast-food joint wouldn't suit your children's sense of decorum better. But don't be put off by its dignified mien. Csikos has good robust food, welcomes kids and shows them what lies beyond cheeseburgers.

Csikos Hungarian Restaurant, 3601 Connecticut Ave., NW. Open from 6 to 11 p.m. Mondays to Saturdays, closed Sundays. Limited parking in garage (enter from Connecticut Avenue). Accessible by wheelchair. American Express, Master Charge, Bank Americard, Diners Club accepted.Call 362-5624 for resercations, which are advisable on weekdays and necessary on weekends.