DD has one very similar to this one that my FIL built her (we're so lucky!), and she and all the other kids who come over really enjoy it. And actually, most of the sites that have that kitchen also have a separate fridge, which might still fall within your budget.
She doesn't really miss having a real refrigerator or dishwasher... at least she's never mentioned it and her imaginative play with it is quite extended.
My nephew has this one from Target, which is wood in the same way that Ikea stuff is wood. It's really cute and wasn't too tough to put together (I was the one who put it together,
).
I just did a quick google search (wooden play kitchen refrigerator) and brought up this site.
She doesn't really miss having a real refrigerator or dishwasher... at least she's never mentioned it and her imaginative play with it is quite extended.
My nephew has this one from Target, which is wood in the same way that Ikea stuff is wood. It's really cute and wasn't too tough to put together (I was the one who put it together,

I just did a quick google search (wooden play kitchen refrigerator) and brought up this site.