It could have lasers coming out of the windows at the top floors

Surveillance.

Tokyo-3

Great news, Giuseppe!  Planning says once we get above 200 feet, the property lines don't matter!

You know how you "solve urban issues"? By helping people in urban areas to have opportunity, life, freedom, choices, love, companionship, community. It's not by deploying tactical surveillance and threat. FFS.

what kind of competition is this? The Hunger Games? Are you really Snake Pliskin?

it’s a fun idea for sci fi porn, but not really practical in a world of drones, satellites, etc.  

For example an underground, relatively shallow lake 2,000 meters (1.2 miles) below the skyscraper part of a city and dimensioned such that the whole high rise district is within its lee may achieve extraordinary reductions in the shocks with which the surface defenses have to contend. The chamber need not be a clear span; very thick natural or artificial columns with or without shock control features would allow a fully supported but effectively vast cavern. Shock transmitted through the verticals must be accounted for, but whatever does escape should diffract upon reaching the top of the support, thus reducing its energy density. Between the changes imparted by the fluid component, the counter shock component, the diffraction of the residual transmitted up the vertical supports, and the non-transmissive cap the power of the shock wave should be attenuated enough to provide critical additional margin to specific structures and sites.

Adapt a Death Ray (design a city of skyscrapers that take out any unwanted intruder by zapping them with concentrated sunlight after the facial recognition software locates them)

this is an exciting and edgy way to address what's usually a boring generic question posed to architecture students. castles and fortifications have such a rich history in medieval cities, and the imagery of defensive buildings is prevalent in sci-fi and fantasy environments. the notion of safety (sometimes offensive safety) is fundamental to our expectations of buildings.

in modern times there aren't many architecturally interesting examples i can think of, mostly radio towers. chicago once had a system of nuclear missiles installed in the public parks which is kind of an ironic usurpment of public space.

https://www.wbez.org/stories/_/b09ed69c-cdf0-4382-a7ac-75480a3d4cb7

in terms of pop culture, look at the way video games invent weaponized buildings. command and conquer's tesla coils are a classic for old millennials like me!

https://cnc.gamepedia.com/Tesla_coil_(Red_Alert_2)#/media/File%3ARA2_Tesla_Coil.gif

in the modern era we use castles as museums and kind of force a cultural reading onto them when obviously they were built for often vile people to do terrible things. now we celebrate that with a name and some decorative artworks, while keeping our functional military installations well-hidden from the public imagination. but thats a reflection of contemporary values which certainly could change in the future.

I'm not going to address whether an urban-watchtower/defensive military installation is actually a good idea for the competition.  That's subjective and you know your professor/studio better than we do.  I'm not personally a big fan but I also acknowledge that sometimes the "unrealistic" directions can pose some interesting questions.  School and design competitions are the time to use your imagination and push boundaries you couldn't in practice.  You'll have plenty of opportunities to claim a "green space" is "fostering community" etc.

If you are going to go this route be careful with your solutions.  It can be easy to fall into the trap of solving certain problems with technology rather than design.  E.G. code (I believe sarcastically) suggested lasers to shoot down projectiles.  That isn't a design solution, it's technology applied to a building.  A tower that creates some sort of force field or shield to protect the city is a technological solution, not a design solution.  Unless you can present a compelling reason otherwise, these sorts of technology could be applied to virtually any building.  This applies even more so when we're projecting future technological advances.

I'd also suggest doing some research into the military/defensive application of a watchtower.  My understanding is their primary use was to create a strategic vantage point for improved visual clarity. They allowed their user to see a greater area, further away, and identify threats earlier.  Is this something that applies to modern times?  In my opinion this has no impact on 9/11. There may not have been a visual connection to the planes but they were tracked through radar, etc.   Would having an extra tall skyscraper watching the planes fly into NYC have made a difference or would they just have had a better view of the tragedy?  Is a modern "watchtower" more about an early warning through information than it is about vision?  Does this get too much into technological solutions?  Before deciding on this direction I very strongly advise you to ask yourself some tough questions.  Put yourself in your professor/juror's position and really be critical.

Good luck with your competition.  I think you're choosing a risky direction as there are many obvious pitfalls.  I hope you're able to navigate your way into something thought provoking.