Ask a coin expert . A dealer . Or get a up to date price guide for the coins in question. 3rd party coin graders like P.C.G.S. Or N.G.C. Have a price guide on their sites . Probably the 3 and 4th suggestion is your best bet.
Ebay
Yes, there are some old coins that are worth a lot of money from countries or islands that don't exist anymore. A coin dealer can check out the coins and give you a price for them.
Banks don't buy old coins, coin dealers will buy old coins, some jewelry stores will buy old coins, banks will take your old coins at face value and then sell them to coin dealers and and make some profit.
Definately Ebay. I can't stress this enough ... do your homework pertaining to your coins. Some coins are far more valuable than you may think because of rarity or a mint mark you may have missed.
Some good sites to research old coins are PCGS.com, NGCcoin.com, and CoinWeek.com. These sites offer a wealth of information on coin grading, values, and historical background.
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One can find a coin price for old Argentinian pesos at your local Cash4Gold store. A dedicated agent will be happy to buy your coins in exchange for cash.
If you meant to ask about running shoes, there are some at the price range from 30 to 50 at Models. I am not exactly sure what your price range is, but Models do carry a lot of old model brand name running shoes at an affordable price.
Take them to a coin dealer for an appraisal. It would be a good idea to borrow a price guide (the Blackbook or Guide to US Coins for US coins) from the library and try to separate the 'good stuff' from the 'junk' first.
There is no patron saint of old coins.
The definition of "old" as applied to collectible coins would vary depending on who you ask. In my personal opinion, a coin may be considered to be "old" at about 100 years. These days, circulating coins are minted with the intention of them lasting for 40 to 50 years in usable and identifiable condition.
Coin collecting is a old tradition of collecting coins of monetary value (money). Many people collect coins that are old, coins that have meaning (like state themed coins), or coins from different parts of the world. Some people do this as a hobby and some collect coins because it will mean their value or worth is very high.