Minimum distance from TQFP to chip cap on PCB assembly?
It depends.  No, seriously, it depends.  There are many factors, and not all of these apply to everyone.

Pick &amp; Place:  Your pick and place machine has limits on how close it can place a tall component next to a short one.  This shouldn't be an issue for this, but it would not surprise me to see an old machine that can't place a large PQFP really close to an 0402.

Inspection:  If you need to inspect the chip then you need to leave room for the inspection stuff.  With a TQFP you would likely only need room for the bed of nails (clamshell) or maybe the flying probe.  I don't think you need room if you have just an optical microscope.  With optical inspection of BGAs this is more important since you need more room for the mirror to sit flat against the PCB.

Soldering:  With normal hot-air reflow this isn't a huge issue, but if you are hand soldering then you need to leave room for the soldering iron or hot-air nozzle.

Whoever you are using to manufacture stuff should be able to give you guidelines on these issues.

Normally, 100 mils should be plenty of room.  When in doubt I would leave at least 100 mils around TQFPs.  In many cases you should be able to get much closer, but I would verify that before doing it.