They feel mistreated and ripped off by the government, and society. More is unveiled later. I am actually still working more on that part. I pretty much have the whole climax down, and all the subplots, but still working on the why. bad social working class, not enough privileges, etc.
I've been told before to use set extensions to make it look like a bigger city, but I'm worried that would just come off as fake or low quality while trying to make a good impression on a microbudget film. I could name a place, but no city near where I live looks anything like New York or Washington for example. The closest that my city can pass for is maybe Statin Island, but I have no reason in the treatment as to why the terrorists are attacking Statin Island only when all the government targets would be elsewhere.
This right here may be the crux of your problem. Lets examine this for a second. You want to make a movie that involves terrorist attacks against the government, which involves at least semi big government and/or public areas. You also want to come off as unique and different so you can stand out at festivals, and you only have a few thousand at best. Am I right?
Using this as your why won't help you then. I've studied political and social theory for years and even developed a theoretical framework for how violent upheavals against the government occur. And let me assure you, they don't occur in the time period we're living in now (at least in the West). Our lives are too nice. Sure, we're upset with the government and want real and fundamental change, but where's the desperation? Is the government rounding up dissenters and executing them? Is there a food shortage? Are people starving? If the answer is no, then you don't have an environment that could foster a SANE group of terrorists like you want.
So, what I'm trying to say is that if you want the kind of terrorists, in which your audience can appreciate and like, you need to create an environment that's suitable for this. In other words, you can't just have them roaming in a modern day city. That modern day city needs to be completely fucked. I'm talking about Poland 1939 fucked. America during the Revolutionary War. Robspierre and the Reign of terror kind of environment. It needs to be intense, otherwise people are going to think their actions are senseless and irrational, just like they do with various groups in the West, today.
Now, your movie would be unique if you could pull off this grandiose movie since not a lot of people do movies like that, but you're never going to do it with a few thousand. So, you may want to consider revising the "Why" part. Maybe, instead of making them the Freedom Fighters we all want them to be, fighting for justice so that their people can live better, why not make them crazy, like the Joker?
You could make a story about one man who was a neurologist and whose also a visionary and sees the social paradigm we're living in as the wrong way to live but he can't figure out why. Then one day, he gets mugged has an intense moment and suddenly feels reborn. So, he goes on to study why this was so and realizes that throughout most of history, we've always lived in a state of fear and chaos, which has allowed us to focus on the moment, rather then dwell on our mistakes in the past or be concerned about the future. Living in the present moment through fear gave us a sense of purpose and reinvigorates our lives. But in the society we live in today, there aren't any natural threats and therefore, we've become a depressed society. You can have a movie about this dude finding a sizable group of young people and have them go off to carry this message.
So, by spreading chaos to other people, they will leave the incident (those who survive) with a cathartic feeling like they're re-born again. This can feed into the phenomenon as to why public shootings occur. Its a venting system to make up for the lack of violence and chaos that reigns in the Western World. If we always dwell in chaos then we'll always appreciate life and we'll always feel alive and in the moment. That's what they want to spread.
So you see what I did there? I literally rationalized a new why that could fit better with your budget. Now, the terrorists don't have to attack government buildings since society is the ill that needs to be corrected. Also, it resonates better with the audience because instead of creating an enemy to go after, it points the finger at them and says "Change your ways and be a better person." Obviously not through chaos but some of the things they can talk about like being in the present moment and never taking a second for granted, etc. And above all, its more unique then creating the typical dichotomy we see time and time again throughout the World. By making your "Why" unique, you're essentially making your movie significantly cheaper and easier to film because their motives will carry the movie, not necessarily their actions.