What sets have the best price per part ratio?
Not going to argue with the reason for the request, but here are some options that give (close to) the best price per part:


Any classic brick box typically gives you a less than $0.05 per part price. Getting those on discount can get you even lower. (E.g. 10704 when on sale at WM in the US was $20 for 900 bricks - or a little over $0.02 per brick).
Special sets not for regular retail (marked as Gear on Bricklink.com) have a good price per part ratio. 40174 Chess set has over 1400 pieces and retails for $55 (~$0.04 per part). Only available at LEGO Shop at Home and LEGO stores. Similarly for the What Am I? game - 540 pieces, currently on sale for $24, so also ~$0.04 per part.
Some smaller sets, especially when on discount, also have great price to part ratio. 100-120 pieces in a $5 set gives a price to part ratio of $0.05 or better.
On the other end of the spectrum: LEGO has released quite some large sets recently with great price-per-part ratios. Sets like Destiny’s Bounty (2300 pieces for $160, Ninjago City (almost 5000 pieces for $300) and especially Saturn V (almost 2000 pieces for $120) are expensive but proved tons of pieces.
Clearance discounts (especially those of 70% or more) are great opportunities to buy high piece-count sets for little money. For example the Imperial Assault Carrier from 2014 was available at WM clearance for $30 or less, and has 1100 pieces.


Brickset has a cool feature where you can see all sets in a Theme or in a given year sorted by the Price per Piece count. First, go to the page for the year you are interested in (I chose 2017). Then use the sorting dropdown to pick “Price per Piece (US)”. You can see that this largely validates my points above. Note that the list starts with many sets that do not have a price per piece in US dollar available (promos, limited release sets, sets not available in the US etc.) You will have to scroll quite far down before the proper list starts.