Eastern Airlines yesterday asked the Civil Acronauties Board to approve a variety of discount fares, including one fare offering "almost unlimited travel" on its system for $299.

The $299 fare would allow two or more persons to travel anywhere on Eastern's 105-city route system in the U.S., Mexico, Canada, Bermuda and the Caribbean, making as many stops as they choose - but at least three - during a period of at least seven but not more than 21 days. Reservations would have to be made 14 days in advance.

If approved, Eastern would also allow one adult to travel at that fare accompanied by two or more children paying $199 each.

In concept, the fare is similar to the Eurorail pass on European railroads, and packages offered by Amtrak and major American bus companies. Some smaller airlines have in the past offered similar plans, but apparently mainly for visitors from foreign countries.

Eastern's proposal which would take effect Sept. 11, also includes other fares:

Individual tour fares to Florida, 25 to 40 per cent below regular coach fares, from many northern and midwest cities, would be available on much less restrictive terms. Travel would be allowed on weekends, the minimum stay would be reduced, and the advance purchase time would be cut to seven days.

Individual tour fares to San Juan and the U.S. Virgin Islands would likewise be lowered and the terms liberalized.

A 7-to-30 day Super Saver fare would be offered between New York, Newark, and Philadelphia to Florida with fewer restrictions and lower fares than are currently available.

A Florida-Northbound weekend fare from three major Florida cities to Washington/Baltimore and 12 other northern cities would be up to 50 per cent lower than current coach fares.

Walter J. Dane, a division vice president, said the lower fares are designed to attract a strong volume of new tourist travel to the carrier.