Yes, holders of an EU Blue Card are permitted to travel to other Schengen states within the EU for tourism purposes without a visa. You can travel to Austria, Belgium, Croatia, the Czech Republic, Denmark, Estonia, Finland, France, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden and Switzerland for 90 days within a 180-day period. As a rule, it is not possible to take up employment outside Germany without a corresponding residence permit.
After you have stayed in Germany for one year with your EU Blue Card, you can leave at any time to another EU member state at any time in order to obtain a Blue Card and work there. and work there. After entering this other EU country, you must submit an application for a Blue Card to the immigration authorities there as soon as possible, at the latest within one month. In order to obtain this, you must fulfill the requirements of that country for the issue of an EU Blue Cardbut this should not usually be a problem, as you have already fulfilled the requirements in Germany.