I've seen people in the past claiming, for example, that it cost an average of $80 to mine a bitcoin (this was before ASICs took over).
Such a figure would be useless. The cost to mine 1 bitcoin varies greatly depending on the hardware you are using, whether or not the hardware is overclocked/underclocked, the current network difficulty and your electricity cost. The cost to mine 1 Bitcoin on a 10 year old single-core processor processor could be in the $100,000 to $1,000,000, while the cost of mining 1 Bitcoin on an ASIC could be <$5, or even "free" if you do not take into account hardware depreciation and don't pay electricity costs.
I am looking for a simple site that just gives me such a flat average cost to mine a single bitcoin based on current difficulty, average running costs (perhaps per country?) and a crude amortisation of hardware costs. Does such a thing exist?
Best thing to do is use the previosuly mentioned website,
http://www.bitcoinx.com/profit/Just fill in the hash rate of the device you are using to mine and enter your electricity cost.
Then use the figures to do the following to calculate the cost of mining 1 Bitcoin:
(1 / Coins per 24h at these conditions) * Power cost per 24h
This doesn't account for depreciation of hardware however.