Need a bike for the month of June in Budapest

teszvesz.hu or vatera.hu or the noticeboards of local shops and supermarkets. But the 1st 2 websites are a sure bet. I've just bought one and found 2nd hand bikes to be more expensive here than in the UK. The cheapest I could find with suspension was 35,000 huf (cheaper to buy new n Tesco) so I ended up paying 13,000 for one without suspension but in reasonable condition.

budapestbike.hu
yellowzebrabikes.com
bikebase.hu

I think all of these places will negotiate longterm rental if you ask. If you google for yourself, I'm sure you'll find more options. Bikebase is the only one I know of that rents bikes that don't have signage on them advertising the company - which may help you blend in better? Good luck!