Costly, expensive, dear, valuable, precious, invaluable, priceless mean having a high value or valuation, especially in terms of money.
Costly, expensive, dear refer to the expenditure or sacrifice involved in obtaining or procuring a thing.
Costly applies to something which actually costs much; it usually implies such justification as sumptuousness, rarity, or fine workmanship.
Expensive applies chiefly to something which is high-priced, especially with the implication of a cost beyond the thing’s value or the buyer’s means.
Both costly and expensive may also be applied to whatever involves great losses or is a drain upon one’s resources, not only in money but in such matters as time, effort, or health.
Dear is opposed to cheap and commonly suggests a high, often an exorbitant, price or excessive cost; usually it implies a relation to other factors than the intrinsic worth of a thing.
Valuable when applied to things which have monetary value usually suggests the price they will bring in a sale or exchange.
Valuable, however, often suggests worth that is not measured in material goods, but in such qualities as usefulness, serviceableness, or advantageousness.
Precious originally came closer in meaning to costly than to valuable, of which it is now a very close synonym. But it carries a heightened implication of worth and often applies to something or someone whose value can scarcely be computed in terms of money.
When applied to a thing of monetary value, precious usually means that it is one of the rarest and most costly of the class that is named, but it may mean that the thing so described is too scarce and therefore, often, too expensive to use freely or generally.
Invaluable and priceless imply worth that cannot be estimated. In practice they are sometimes used when precious is actually meant but would seem not quite in keeping for one reason or another. Therefore their use tends to be hyperbolical and often, especially in the case of priceless, intensive.