Thought experiment involving Computer in an engineered gravity well Suppose we have a computer at some location in space within Earth's Orbit. 
One can look at the all the gravitational forces being exerted on this device (one from the earth, smaller forces from the moon, sun, etc... ) 
If one places small, high density objects in a direction opposite to where these forces point (from the computer) you can arrange it so the computer experiences less gravitational attraction/potential in any direction. 
Does a computer under these conditions run faster, since it is technically in an area of lower gravitational potential, so its clock should run quicker. 
And that leads to the natural question if one can identify all the gravitational sources aorund an object (of increasing scale, say planetary, solar, galactic, inter-galactic), and cleverly put black holse around the object to counter these forces exactly where the object is. Can they essentially artificially boost the speed of a computing device this way? 
 A: You say:

you can arrange it so the computer experiences less gravitational attraction/potential in any direction

but the problem is that the gravitational force and the gravitational potential behave in difference ways so a zero gravitational force does not mean zero potential. Let's consider a setup like one you describe:

For any gravitating object the force (per unit mass) is given by:
$$ F = \frac{GM}{r^2} $$
and the gravitational potential by:
$$ U = -\frac{GM}{r} $$
Force is a vector and has a direction, so as you say we can arrange our masses so that the gravitational force they produce balances out to produce a zero net force. However gravitational potential energy is a scalar and simply adds together. So while the net force on our observer may be zero the gravitational potential is not zero and is given by:
$$ U = -\left(\frac{GM_e}{r_e} + \frac{GM_m}{r_m}\right) \tag{1} $$
The reason this matters is that the time dilation does not depend on the force - it depends on the gravitational potential energy $U$. For weak gravitational fields the time dilation is given by:
$$ \frac{t}{t_\infty} \approx \sqrt{ 1 + \frac{2U}{c^2}} \tag{2} $$
Remember that the potential $U$ is negative (see equation 1) so the right hand side of equation (2) is less than 1 i.e. time runs slower. Every extra mass you bring in to balance out the forces just keeps making the potential more and more negative i.e. by bringing in the extra masses you are making the time dilation even large not reducing it.
A: Suppose there are 5 gravitational forces acting on the object and you bring a 6th body to counter balance them. 
Now, the object is under influence of gravitational field of 6 bodies, not 5.
One special case of gravitational time dilation is - "Time Dilation in a gravitational field is equal to time dilation in far space, due to a speed that is needed to escape that gravitational field"
By putting the 6th body, you have increased the escape velocity - i.e. you have increased speed that is needed to escape the gravitational field. Therefore, you have increased time dilation.
