The Hague or Rotterdam? pros and cons

Welcome on board and welcome to the Netherlands soon 

It depends on what are you looking for and what you like.
Both cities are great in their own uniqueness. They are big, you can shop until you drop,  nightlife is great, both are multi cultural, lots of activities etc. Good public transportation and both cities are well connected.

The Hague is the city of diplomatics, the international court, the parliament residents here and it's close to the sea. Scheveningen at your feet where you can eat the most fresh fish you'll ever had in all its various types and ways to prepare.

Rotterdam has the third (?) biggest harbour of the world and has an impressive bridge to connect both half sides of the city.

If you are talking about prices and housing,  they're similar.  Like I said, depends what you are looking for and how you feel about their vibes.

Thanks @Primadonna

Somethings that I would say that are important to me are:
1) green in the city (not just buildings). I really love when the green is integrated, not only parks or protected areas.
2) pedestrian zones (Auto-free)
3) expat support/community
4) openness from locals (I know that I need to speak the native language for full interaction)
5) variety and easy access to parks
6) accessible nightlife
7) infrastructure to grow (not those cities that grow but get worse)

PS: Rotterdam is actually the third busiest port from world, but about size it's the 10th (1st of Europe).

Discover both cities trough Google earth.

Locals are probably better accessible in Rotterdam (and in English!!! 80% speak English in Nethelrands) and for nightlife, of course, Rotterdam is better too. As said above, The Hague is an expat life (not international, but expat, it's not same), who are diplomats, who work in International court or for Parliament so, it's a city very "stuck", upper-class, quarantine, so not a lot of young people, not a fun town. And moreover, it is ugly, with none charm.

Rotterdam is opener, inhabitants originary from more than 180 countries, young, with University, and city centre and some districs with little channels are very nice

Given your list of preferences, and reading the suggestions you've been given so far,
I would start by discovering Den Haag through Google earth first