Do a good job. With all the time you save, you can focus on doing things with drones or AI or whatever you want. Then inevitably when the scope of those projects goes out of control you won't have the stress hanging over you of it being for school and will be able to explore the domain with a light heart!
I wouldn't do the website as a matter of principle.
I helped build a website for a department when I was in college. I was paid a reasonable hourly rate in exchange for my services. In this case, the OP would be paying the university money in exchange for the privilege of building them a website. That's insane.
This attitude is common amongst my peers. I don't understand it all.
In general any time you do something for CS it's either trivial or if you had some qualification to back you up you could get paid; you're not paying for the privilege of designing their website you're paying for the support, guidance and ultimately assessment of your skills.
There is a problem of larger scope which is that education at a school level has been poor or non-existent as side effect of this is many people self-teach and then start university with skills way beyond their peers, web design is a good example of this because it's a relatively open platform that's easy and fun to get into, the result is that most universities must start from no assumed knowledge in the field.
It's only because you were able to teach yourself webdesign that you feel that the task is beneath you. If you really want to address this problem you need education to be better across the field so that university level can address significant tasks rather than filling in the basics for the first 2-3 years. This is starting to be addressed in the UK by the likes of the Raspberry Pi foundation and at a government level by mandated CS education in primary school but without incentives for teachers to take up the subject I don't know how effective it will be.
definitely agree with you, I think I'm the case you are talking about. I came to uni with a bigger experience and knowledge than other guys, I don't blame them. But I don't want to put myself on their level that's why I'd like to propose my own topic and show my skills there
If you're doing it to show a future employer, then a full-featured modern website with cleanly written code is a great work example. (Though a deep-pocketed institution might consider paying someone to do this type of work.)
UNLESS you have a specific domain you want to work in. Or you have a company you want to get a job at and they work in a particular niche.
I also agree with zorrb, as I used to be plagued with wanting to go above and beyond with every academic project. The problem is you have limited time, and you can find a better use for it working on something that is more flexible.
It also helps to begin with a strong interest in a specific field, and extra knowledge to back it up, so you don't waste a lot of time doing introductory research to get up to speed.
If you're here, then you're likely more entrepreneurial. Do the easy project, and spend your extra time working on a start-up idea or connecting with classmates to find a co-founder for something bigger.
Do a good job. With all the time you save, you can focus on doing things with drones or AI or whatever you want. Then inevitably when the scope of those projects goes out of control you won't have the stress hanging over you of it being for school and will be able to explore the domain with a light heart!