Let me know what dates so I can put it in my calendar! I have a bunch of suggestions. It mostly depends on what your preferred method of transportation is, how much you wanna see and how much you're willing to spend. While Amsterdam itself is pretty good to base yourself in, I have two less popular, train-based options: The Hague and Brussels.
The Hague has direct trains to Amsterdam Airport (30 minutes), Amsterdam (40m), Utrecht (40m), Delft (13m), Leiden (20m) and Rotterdam (20m) as well as Antwerp (67m with Thalys high-speed) and Brussels (2h with Thalys), all cool to visit if you ask me. It's a seaside city with a long urban beach to cool down in the summer. It has the Parliament, a great city center and because of all the politics there it's internationally-oriented.
Rotterdam, Leiden and Utrecht are also good places for similar reasons but each city is different. Train tickets are usually around 10 to 20 euro per person each way, highspeed trains around 30-40 if you buy them a few weeks ahead.
If you wanna see more of Europe and don't mind a bit more travel, Brussels might also be a good base. Amsterdam is 2h10 with highspeed trains, London 2h30 and Paris less than 2 hours.