Shinjuku/Shibuya alternatives?

Looking into a 5 night stay in Shinjuku but it's coming up crazy expensive, even after the Blossoms and Golden Week!

I'd like to be near the tourist bits (first timer) and good for transport around, but are there any neighbourhoods near Shinjuku or Shibuya that are near stations but don't sacrifice too much on bars/shops/attractions?

Perhaps areas that might be a little cheaper?

Thanks