Let's say the bad guy has a Wand of Fireballs, and wants to blast the party with it. To do so, they must:
...use an action to expend 1 or more of its charges to cast the fireball spell ...
The party wizard wants to stop this and uses Counterspell which says it:
You attempt to interrupt a creature in the process of casting a spell.
My thought is that this won't work. First, let's remember that when a character casts a spell, they use the Cast a Spell action. There are always components involved, whether verbal, somatic, and/or material.
Using a magic item requires none of these things...it just takes an action. But...what kind of action does it take to use a Wand? Well, according to the Player's Handbook (Combat > Actions in Combat), it would be the Use an Object action (emphasis mine):
You normally interact with an object while doing something else, such as when you draw a sword as part of an attack. When an object requires your action for its use, you take the Use an Object action.1 This action is also useful when you want to interact with more than one object on your turn.
Lastly, the spell description for Counterspell says that in order to cast it, you use your Reaction:
which you take when you see a creature within 60 feet of you casting a spell
So, while the players could certainly see the bad guy with the Wand, they'd see him using the Wand, not casting a spell.
I looked around this Stack, and didn't find this question - which seems a little strange. There is a question (Can you Counterspell a spell-like ability) that deals with spell-like abilities, but not magic items.
To keep the scope of this question narrow, I'm just asking about magic items that state they require an action to use and their use casts a spell.
Can you Counterspell a magic item?
1: The DMG basically has the exact opposite wording regarding the activation of magic items (Ch 7 > Activating an Item) found here. Not sure why these two core rule books directly contradict each other - hopefully that'll be addressed in a Sage Advice someday.