day care for 1 yr old

No idea what current pricing would be here.
I suppose if you want a staff that speaks English you will be paying more.
Why would you want to enroll such a small child in school in a new country if you yourself are not aware of how things go?
Just saying, I'm old school, never allowed anyone to baby sit my son except once my trusted neighbor who had 2 small kids herself in Hawaii and my mother. No one else was allowed to watch him. I had a rule of no one watching him until he could speak and let me know if anything was off.
I actually only went out his first year once when my neighbor watched him, had to go to a movie , so everyone told me.
I was attached to him and nursed him for 13 months until my mother told me it was time to stop it.
Schools do tend to not care as much as a parent does of course not everyone is over protective like I was.
Here in Hungary under the communist system you could find day care for a 2 week old infant if working was more important.
They used to pay mom's to stay home but only about half their normal wages.

Hi Priyanka!
There are day care facilities from an early age. It's called bölcsöde and every city and town has several of them. Private ones tend to have a website where you can check how much it costs, it depends on what they provide: language is the most common extra that's offered for these very young children.

State day care will accept your child as well, where you have to pay for the meals, a few hundred forint per day I think. In Budapest you're likely to find a carer who speaks some English but don't hold your breath that they will be "English speaking". It's not the main pinnacle of their job to speak languages, they train and care about the healthy development of young children and anything on top of that, like speaking a foreign language, is a plus

I'd go to Google maps and search for bölcsöde where you want it to be, then stroll around to see where it is and what you think of the garden and watch the kids a bit, how the carers react to the children etc. I'm very happy with my son's day care and he had a box in his class whose parents didn't speak any Hungarian. Not a bother on the little man, only grown-ups fuss about grammar. 1-year-old children communicate in several means, language is not one of them for most

Good luck!