I find a useful way to think about specific heat is this:
How much heat does the substance contain at room temperature? If it contains a lot of heat, adding or subtracting a small amount of heat will not make much of a difference. However, if it only has a little energy, removing the same amount will make a big difference, causing it to to cool or heat quickly.
Salt/ sugar water contains less heat than water, so it cools and heats quickly.
The ions "trapping" water molecules plays a role, but there is another, more simple explanation: the dissolved substance also physically gets in the way. Imagine a bunch of children running around in a space. Now imagine you added some rather fat people at random spots. The children would bump into them, and slow down.
Roughly speaking, heaver substances have a lower specific heat, take a look at this graph: http://periodictable.com/Properties/A/SpecificHeat.html
The more massive molecules move more slowly, hence less energy, hence, adding or subtracting energy is a big deal. However, this explanation is simplified. If heavy molecules moved at a speed proportioned to their mass, they could still move in the same pattern as light ones. However, they don't. Everything else being equal, heavier molecules are bigger, which means they run in to each other more. Its not actually the speed but the size that is most important.
Final answer: Salt and sugar water have large molecules in them that slow movement.