I got tired of asking for certain checks in the game. I felt like I was giving something away by saying "Ok, give me a nature check" so I decided instead, when asked a questions that I deem a roll is relevant to ask them "What skill would you use?"

I told them before the last session started that they would need to tell me what skill they thought was relevant, and depending on the roll and how adjacent that skill is to the query, I would tailor a description accordingly.

Of course everyone wants to use their highest modifier. So I reiterated that the skills they choose need to make sense. Trying to figure out a magic item by perception alone will only work if you see the item actually being used. Athletics would probably be a bad choice, maybe you break the item. Of course, if you want to use Investigation to figure out if an NPC is actually a Fey creature, that could work, however it would probably take more time than a just your turn.

What do you all think? Suggestions? Criticisms? Ideas?

I don't actually invite players to make skill checks. I ask them what their characters are doing, and they respond with descriptions of in character action (i.e. no one at the table says "I want to roll [insert skill name]").

The only time a roll of any kind gets involved is if the outcome of the player's described actions has an uncertain result, and in that case I offer the player a thing to roll and the possible results, which the player can take and make the roll or suggest changes to the details if they think something else would be more fitting.

For example:

DM: "The room is furnished as a study, a desk and chair roughly central in the bookshelf-lined far side of the room, with a small couch with comfy-looking pillows along the wall near the door. There are no obvious exits other than the door you've entered from. What do you do?"
Player: "I go to the desk, rifle through any documentation or containers upon it, and then I'll do the same to the drawers."
DM: Knowing there is a false bottom to one of the drawers that might go unnoticed, "Alright, there is something to be found, so how about a DC 12 Intelligence (Investigation) check; pass and you've found it, fail and the whole party is as confident as they can be there isn't anything to find and stops looking (at least until new evidence of some kind is found)."
Player: "Can I make that a Wisdom (Perception) check instead?"
DM: "Sure, if you raise the DC to 15." <then the players rolls what they agree on>

Of course, I run my games with as much transparency as can be done (I don't tell the players literally everything, but I also don't hide or obscure any detail that is just the mechanics/rules of the game being played, and especially never have them roll a die without knowing what that roll means for them and their character), so this process might seem really odd to anyone not being as transparent in their DMing.

Aaron, we are on the same page for the most part, but I think you've missed my intent.

First, I never skill lock a story element. If it's important to keep the story going, it will happen/be found after 5 or 10 minutes if the group missed some clue in my description or if they are otherwise struggling for an answer. I will skill lock something like a treasure, or secret passage around a trap etc. If you miss it, you just miss it.

Second, I feel like telling a player "give me an investigation check" makes the player feel like they have to find something rather than could find something. Which is an important distinction, at least in my opinion. I know there is a false panel in the wall, and I know there is a small chest with 10 platinum and a healing potion. It isn't that important. It's fluff.

My intention is to give the players more opportunities to role play and interact with the world by trying things out of the normal box. Tell me how your skill applies to this situation and the information you are trying to get. Tailoring my response to the skills they decide to use.

DM: "The room is furnished as a study, a desk and chair roughly central in the bookshelf-lined far side of the room, with a small couch with comfy-looking pillows along the wall near the door. There are no obvious exits other than the door you've entered from. What do you do?"
Player: "I go to the desk, rifle through any documentation or containers upon it, and then I'll do the same to the drawers."
DM: Knowing there is a false bottom to one of the drawers that might go unnoticed, "Alright, what skill would you like to use."
Player: "Can I make a Wisdom (Perception) check?"
DM: "Sure"

Mechanically the same. The only difference is I never tell the players what I set a DC as unless I'm running a skill challenge type scenario. Again, I feel like that makes them feel like they have to find something. 

Quote from TheGoodKingAzalin >>

Aaron, we are on the same page for the most part, but I think you've missed my intent.

I haven't missed it, I just have a different intent of my own that I was sharing. Just sharing ideas, not criticizing your method at all - it is a fine method, and is one I'd likely use if I weren't dedicated to transparency.

I also don't skill lock progress, though I didn't use an example that demonstrates that. If whatever was in this hypothetical false-bottomed drawer were necessary for progression of the adventure with the players having fair odds of success, the odds presented to the player would have been something like "pass and you complete your search uninterrupted, fail and your search takes long enough for your situation to become more complicated."

And I understand the feeling that giving the players certain information makes them feel like they "have to" find something, but I solve that problem differently. Instead of letting them feel like a die roll might not actually mean something important (an unacceptable condition to my table full of players as a direct result of their DM prior to me abusing DM privilege to ignore dice rolls to an extreme degree), I make sure that they know they can't just keep trying and why (the in-character reasons, since the out-of-character reason of "the die roll doesn't matter if you can just keep trying until you succeed without any consequences" is obvious). Which is why I stated the fail condition as being confident their isn't anything to find, rather than just not finding anything - players aren't prone to say "I'll try again", or to have another character try, when they've been told their character is confident in their search being fruitless due to lack of fruit, where "You don't find anything" provides them no such reason to stop looking.

I mean, if they say that they are going to rifle through the desk, they are investigating it. You aren’t giving anything away by asking for an Investigation check after they say they want to check it out

Oftentimes I won’t even have them make checks unless requested. There is no point in requiring a skill check if the end result is the same. For example, if I want my players to find the letter on the desk, I’m not going to ask them each to make an investigation check.  I’m not even going to make one of them make it, so long as someone says “I’ll take a look around.”