Yes. The rule of thumb is that if you are the citizen of one country traveling into another country in which you do not have citizenship, you need to get a visa. There are some exceptions (for example, West Africans can travel between West African countries without a visa as long as they have a passport from a West African country, and I believe people with passports from a nation in the European Union can travel to other countries in the EU without visas), but as a US citizen traveling to two separate places in Europe, you will need visas for both countries.
