What's the average rent for a 2-bedroom apartment in Russian Hill?

That seems high to me. I've been looking at apartment prices in the are and finding most of them to be in the $3000 range and even a few down at $2800.

Maybe home prices are included in that average?

I don't think $4000 seems high for a 2-bedroom in that area. I've seen a lot of 1-bedrooms that run $2500-$3000/month. I think it might be difficult to find a good 2-bedroom that goes for under $3500. Taking an "average" is also tough, because the apartments in that area have such a range of rents. It could be from $3000 to $15000, depending on what you're looking for.

On average, per month it will cost between $4000 to $5000 for a 2 bedroom apartment in Russian Hill, San Francisco.