The battery on my Jeep Grand Cherokee goes completely dead parked overnite. The battery and alternator are new and check out good at the parts store. I sometimes hear a faint clicking sound even when the ignition is off.. What could be draining this so completely?

Sounds like a charging system problem and the alternator may not be working. The gauge light will come on if the charging gauge is showing low so you will look at the gauges. Have the battery and charging system tested

If you are not using the vehicle except during the summer, You should really have a battery tender (2amp automatic charger) attached to it. There are normal items that will otherwise drain the battery over an extended period of time (radio and clock to mention one). If you jump started it when you found the battery to be dead, it's possible to have the alternator fail as it cannot charge a dead battery
(alternators are designed to maintain the state of charge, not re-charge. If "requested" to re-charge they will run full on and eventually burn out).
Auto stores often do not have experienced help. Therefore, it's possible that your alternator may still be OK. First, completely re-charge the battery and have it load tested to make sure it's good. Then, do a quick check using a volt meter. Running voltage measured at the battery terminals should be between 13 and 14 volts. You should see a drop with all accessories on including headlights on high, but the voltage should not creep downward even after fifteen minutes. If after running, you start seeing numbers below 12.9 the alternator or regulator is bad. (regulator is part of the computer so hopefully it's not bad).
Good luck!!

Check for a more than .2A draw when the car is off using an inductive ammeter with your own tool, or at Sears or Walmart or your local auto parts store (if they are so equipped).

How old is the battery in the car? Batteries only last 3 years on average, I learned at Sears, through observing warranty adjustments.

Either there is an external draw on the battery or the battery is internally shorted.

Good luck on this repair.

Do you have an alarm? It's common for them to pull too much current and drain the battery. Also look for lights such as dome lights or brake lights stuck on that could drain the battery. Are all the wires to the alternator and battery connected?

First, it can damage your alternator to try to charge a dead battery by just driving or running the car. The alternator is designed to maintain the state of charge already in a battery.
Old (pre mid 60's cars with generators could do that).
Have your battery charged and tested. if it checks out, then have the charging system in the car tested. On most newer Jeeps, the regulator is not in the alternator it is part of the computer. If the alternator checks as good but it is not charging, that may be why.
Hopefully you just need a new battery.

How can the Alt and Battery be good, but not charging? The Voltage Regulator is inside the alternator. Keep out of the Parts Store and take it to a shop and have it checked on the truck. you may have wiring issues.

Have the alternator tested,remove it,and take it to the auto parts store,if it test good,replace the computer,the voltage regulator is in the computer.

First: Are your Battery Cables (inside) and Battery Post nice and shiney? It is amazing how corroded/oxidized cables and post will kill a battery. Get then bright and shiney.
To test the Alternator. Start the Vehicle. You can Jump it if you have to. With the Engine running, disconnect the Negative Cable from the Battery. If the Engine dies, it is a bad alternator.
Was the "new" Alternator new or remanufactured?
Was it the correct alternator inespecially 'amps' for your particular vehicle?
Take the "new" alternator off and have it tested at auto parts store where you bought it.
Any remanufactured alternator may pass the factory inspection but will fail at the auto parts store. Just because it came out of a new box, and looks new, doesn't mean it works new.
Always when buying and part with a "motor" attached to it from an autoparts store, insist that the new one gets bench tested.
If this does not fix the problem:
Are your belts slipping? Worm out, loose or slipping belts will not turn the alternator pulley correctly and draw the battery dead.
Inspect the Red Positive Wire coming off the Alternator back to the battery. Look for any burnt, melted, or shorted areas.
The Battery Starts the vehicle. The Alternator runs the engine and trickle charges the battery.
Let me know if this helped, or if you have addtional information or questions. Feel free to contact me at FixYa.com!

Check the fuses for the overhead console, could be that if not then the console needs to be replaced.....

Have you had the alternator checked?