Before would I always eat pizza for my hungover. Then I noticed my belly started to grow, so I had to quit it (as I had hungover every other day..)
But still I eat sometimes pizza, and if you aren't trying to stay slim, if you want to live, I have some tips where to search for decent pizzas!
1st thing is that because you are on a budged, you should head to Kallio. They have dodgy pizzerias in Kallio, which look like you can buy sex from there too, and then they have decent pizzerias...
There are so many restaurants in Kallio, so you have many options. My favorite is Mäkikupla and Cafe del Mar. Especially I recommend Mäkikupla, because they have many vegetarian options. Both them have pizzas for around 7€.
Also there's a Italian restaurant Mare Chiaro, which is a more like a cult place. They have been serving Italian food from the 80's in same place and Mare Chiaro's customers still love it. And it's cheap! 5-7+€....
Mäkikupla: Torkkelinkatu 2 (metro to Sörnäinen, or trams 6 and 7B, hop off at Käenkuja)
Cafe Del Mar: it's just in Karhupuisto (trams 1A, 3B, 9, or metro to Hakaniemi and walk to Kallio)
Mare Chiaro: Hämeentie 20 (trams 6 and 7B, hop off at Kaikukuja)
Also there are pizzerias which serve pizza until 5 am, one this kind of place is in Viides Linja, I just can't remember it's name... Very close to the sex shops!