You could say you're fixing it or it's the "phone graveyard"
If you have other dead/useless phones, mix them together and I doubt she'll check them all.

Remove the battery/sim and store that somewhere you keep small electronics/batteries.

... my hobby phone because it's with me everywhere I go.

My phone is double password protected, so if anyone finds my phone, they need to know the 2 passcodes just to get to the main screen. If the phone is ever lost or stolen, I can track it down by GPS and manually shut off the phone. The phone then becomes bricked.

Just about everyone that I know have their own cell phones, no need for them to use mine.

Serpius

But seriously,

Best to never have it in the house.

Keep it at the office, or maybe in a LOCKED glove compartment of the car.

Never leave it in your clothes.  All wives go through pockets all the time.

a friend of mine once told me he hid his in an old golf bag.  There are all kinds of places to hide it, but it seems to me, away from home is the best idea, somewhere your SO does not have access to.

Swim

Good one...  *chuckle*

Buy a gun safe for your car and keep it in there.  I have kind of a cheap one, but you can get them with fingerprint recognition.

That's before I started to use Google Voice. I now use Google Voice when I hobby and delete it when I am not.

If you don't share a car with you SO, then the spare tire compartment I have heard is what some gent's do.

Don't have an SO but had a very nosy mother when I go home for break so I have to keep always hide it in a different spot, thankfully her cleaning habits are as habitual as they come.

In general, a noggy phone should not enter your shared living quarters...  playing with fire.  That said, I have brought my hobby bag in when the house is empty, as I'm arranging a meeting.  A 'hobby bag' might contain said phone at times...  but 'hides in plain view' because it's a twin for a tennis bag, golf bag, tool box, carry on bag, gym bag which you would likely been seen carrying.

When not in use...  hobby phone should be shut off...  some remove battery too.  And stored.    
Ideas I've heard:
I think autos are riskiest if you ever ride together or might swap cars when one is in the shop.  Spare tires bins aren't always dry & what if SO has a flat?   I have my eyes open for a car spot but haven't found one I like yet.  
Work shop in a jumble of old electronics, saved for parts.  
A locked tool box  
A coffee can in the sawdust bin...  
Locked drawer in your office at work.
A hollowed out copy of Grey's Anatomy (reportedly used by CL Killer)...  actually thinking of Chilton's Auto Repair through 1977.  

The thing is if it looks like it's hidden and then discovered, it's already provided the information that it was hidden.  
A deactivated phone will still call 911 (required by Federal Law).  So a phone in the car, could be an emergency phone.  

..someplace she's never been.  I took her into the kitchen."

Having a hobby phone AT ALL is a risky proposition. Most people keep their phones for a while (years?) - the discovery of a strange phone will not be easily explained.

No matter how out-of-the-way you think your phone is stored, that won't stop a wife from one day saying "I'm going to throw out that old golf bag/clean out that unused drawer/etc" And of course she will look through it before throwing out the bag or cleaning the "hidden" drawer.

Hiding in a car is even worse, as you may think you never swap cars, but one day your wife's will be in the shop and she will quickly borrow your car, without asking. Or maybe she does ask, and now you're left stuttering and sputtering...

How about not having a hobby phone? Unless you wife goes through the phone bill with a fine-toothed comb, but in this day of unlimited minutes, who does that? Or learn how to use Google Voice from your phone, so those calls don't show up on your bill. Same for texting - there are tools out their that use your data plan for texts, so they don't show up on your bill.

Agree with all this, plus the comment "The thing is if it looks like it's hidden and then discovered, it's already provided the information that it was hidden."

My hobby phone hides in plain sight. It's my regular smart phone. With unlimited text and calls, no one looks at all the numbers called or tracks the texts. Texts can go through an app, phone through google voice.

All that said, the Petraus case shows that you leave electronic tracks, no matter what you do. Just don't become the head of the CIA...

I agree with both posts.  Your SO knows every inch of the house and it is only a matter of time before she finds it.  Any reason you can't leave it at the office?

And don't think for a moment that your SO wouldn't go through call records and bills.  Any SO who thinks they are being cheated on will suddenly become a forensic scientist.