I've never had a guitar with a floating tremolo before, but I hear that some styles will go out of tune easily.

Is the best way to test it just to bend notes like crazy, dive bomb, pull up, be pretty aggressive with it, and then afterward see if the guitar is still in tune?

How much leeway should one expect from a "good" floating tremolo?

If you pull higher than three half steps, you will pull any guitar out of tune.
Dive until the strings flop off the fretboard completely slacked.
Keep in mind the strings may not be stretched out yet, so do it for a while and then retune the guitar, then go at it.

Yeah - If you are going to a place like Guitar Center, just grab the guitar (or if it's top shelf, like a JEM, just ask, they will.) and convince them to give you the trem arm out of the drawer. What I would do, is start with a few dive bombs, you should be able to completely take the bar down to the body. Don't worry, the springs won't brake. If they do.... well, the guitar must've been too low quality and you're glad you're really testing the trem .
If it stay in tune, go for a few pull-ups. You can probably pull up a 4th 0 that means, the G will be a C (or the 5th fret). It may fret-out before it reaches that, and thats fine. After a few pull-ups, dip the trem, or bend the strings, and see if it is in tune.
After this, it should still be in tune. I only need to set the tuning on my RG520 (original edge) once a string change, which means about once a month.

I was at a GC recently and got to go over a variety of Ibanez guitars across all ranges. Here is a breakdown of the most important ones I tried:

• RG4EX1. This is a GC (and some other retailers) exclusive. This model has the Edge-III trem, and after I have had my RG520 with the original Edge for a year, I could certainly tell a difference. Even though the trem angle was correct and the nut seemed tight, this still couldn't even stand basic trem use. The arm that comes with the Edge III also feels very weak, I would question it's durability in a live setting.
• RG350DXMZ - This is a newer addition to the RG line, this is like the long-standing 350DX, but it has a maple board and a Edge-Zero-II bridge. I like this one a lot. Even though, it should be similar to the RG4EX1, the quality seemed a step higher, in fact, the only thing the seemed the same were the INF pickups, which were very poor comparing the to DiMarzios (which I did in that same visit). But we are talking bridges here - and the EZII does not disappointed. I would not be upset about getting any guitar with this bridge. It has the Zero-point system, which Ibanez has improved, and is easily removable. The arm is good. It's not the standard push-in type. There are two push-in types, the first generation, which is like from the Original Edge, which has bushings for a tight fit. The second gen, is the kind like on the Edge III. Those are generally unreliable and can get loose with little or no remedy.
  But this - the EZII - has a threaded collar. Now, Ibanez tried this with the infamous Lo-TRS-II, but don't worry, this on is much better. If I rated the Edge-III a "1" and the original Edge and "10", the EZII would probably be a 7 or an 8.
• I tried a few Premiums - awesome workmanship. These also come with the EZII.
• Ibanez JEM7V - you knew it would have to come to this, right? Well, this has the original Edge, which I already mentioned I have on my RG520QS - so the performance there is the same.... flawless.
  Also, the JEM neck is sweet. I didn't think it could get much better than the original wizard (not a wiz-II fan), but the JEM neck carve is really awesome. It can accommodate technique very smoothly. I believe that may have something to do with the fret-wire being a little different. Either way, awesome player.
  Also, don't believe what you've heard about the Evos... I was skeptical, but the are really really sweet sounding. They may not be very versatile, but it has the Vai thing completely mastered... which I guess only makes sense. It also sounds great through a Mesa.
  

So, when trying bridges, you need to think, "can this get me through a show". You shouldn't have to retune, especially a Floyd, through a show. Try playing a few some you know that are very whammy-bar-ish. If you can do that for a while and it not go out, then your good.
Like I said, I never have to retune. Neither should you.

Also, consider going used. If you are going to a GC, they normally have some old Ibbys. That is how I scored my RG520QS in the first place. MIJ Ibanez is hard to beat.

Ask for a bar, plug in and abuse the F**K out of it!

There are ways to make any decent tremolo great - locking or not. Different ways to attach the strings to the tuners, minimal friction at the nut and tremolo posts - those things might not be good in a store due to improper setup and nobody has bothered giving them much attention before they are sold.

Thats what I said.

I may be a freak but I bring my own sh!t when I am going to try out gear. I do not have the patience, especialy with cables. Those things are screwed down and never reach the amp I want to try.

I bring:
* My own cable
* My own whammy bar (if needed)
* My own micro fiber cloth
* My own pocket multi tool with allen wrenches, etc

All the stores know me so they don't mind.

Get naked, then shake it hardly