Sudden drop in water pressure at sink furthest from entry of main water line
This is normally caused by rust, scale or other debris clogging the aerator on the faucet, remove it and see if you have normal flow, note without the aeration the water stream will shoot like a garden hose so be prepared. If the flow is still reduced the orifices in the valve may be plugged by the rust, scale  or other debris. Washer less faucets tend to have this problem more often than standard valves. 

To fix a washer less turn the supply lines off remove the handle and cartridge , I put a bowl over the fitting and turn the cold on for a few seconds then the hot to purge anything in the lines out. Sometimes it is easy to clean the cartridge or plate other times a replacement is needed, if you just clean it is a good idea to change out the o rings with new ones many times they are color coded but if not they are standard sized and can be replaced with generic buna o rings. 

These are the 2 places I have found problems that cause low flow on many occasions both with city water and well water systems.