We travelled to the Baltic ports in May. The countries visited have thriving economies and unlike many other ports of call do not rely on tourism. They either have their own currency or the Euro and will accept dollars in exchange bureaus or banks but not in shops.
My recommendation is to take a small amount (approx $20) in local currency to cater for taxi/bus fares (or a beer or two) and then to either exchange additional money into local currency or use a credit/debit card to shop or via an ATM.
I am not trying to be judgemental but 'the world is your oyster so try to embrace it'.