often I'm not allowed to play guitar at certain hours of the day so I'd need a device the would simulate an amp but it has a headphone output so that I can use that. Something like a Kemper Profiler, but that is way overkill for just practicing. I mostly play metal and rock if that is a factor.
I don't have a clear budget in mind since I don't have a clue what it takes for such a unit to sound decent.
Sounds like a Line 6 Pod will be right up your alley. Either the newer HD models, or if you're really looking for the budget option, their older models are fine for practice too. The bean-models will be cheapest and have all the features IIRC, but a floorboard might be more practical.

I'd highly recommend shelling out the extra money for the HD-series, though, and I'd also recommend the floor-models. If you ever want to use it just for effects, it's way handier than having a bean model laying around.
I will look into that, watch some reviews and stuff. Thanks for your answer
I forgot one thing though: do you only want to play with headphones, or would you like to have a speaker as well just in case you want to jam with friends? In that case, something along the lines of a Peavey Vypyr VIP, preferably the 2 or 3 because of the larger speaker, would be nice.
No i would only use it with my headphones. If I jam I use my Marshall jvm 420 h and I would only use the POD as a multi effect processor
A Pod HD can become the front end for anything up to and including a gigging setup.

If you want to keep the budget (and the size) very small, however, you might want to look into a Korg Pandora PX5D or a Pandora Mini. MORE than what you need to practice with and it'll fit into your pocket (or the accessory pocket of your gig bag).
I'd suggest looking into something like a Pod HD floorboard then, given that you'd use it with your amplifier as well for the effects it offers.