Im curious, how does being a "New Newbie" differ from merely being a newbie?
First, I'd ask you to first top saying you've found 'nothing important.'
You are doing what many dont know how to do - you are searching for far horizons, for something beyond crappy Flava Flav reruns. I congratualte you. Keep at it and I assure you that something important WILL come along.
Second, dont plan trips to far flung places until you have researched and searched your own backyard, your own town and your own locale. It has been said that there are more places within five miles of your home than you can search in a lifetime. Spend some time learning about them.
Third, know that much of Arizona is open and you can detect; but much is NOT, surprisingly. Find out about that.
Here's something that I penned awhile back; read it and tell me what you think:
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"Dahut's Secret Tips to Success...for Newcomers"
or New Newbies 
1. Equipment is NOT the answer.
The other, more crucial element is MINDSET. We tend to be techno-dependent, expecting gadgets to do all things for us. Guess what? People were finding treasures before detectors came along. The difference is they knew what to look for and had some idea where to find it. You should do the same. Do buy a quality detector, of course, then consider it merely the means to an end. As I like to say, "Know Before You Go."
2. Dig, man dig!
You wont find anything if you don't and you won't learn what your machine is telling you, either. Your goal is to become an "object recovery specialist," not an expert at merely locating objects.
3. DO NOT rely on a meter or display.
There is a mountain of hype that claims this detector or that detector can tell "trash from treasure." DO NOT believe it. There is A LOT of junk out there and most of it masquerades as good stuff, especially to the newcomer. You will find trash and plenty of it, so start developing a cavalier attitude to it early on. When in doubt, see, TIP #2 .
4. Turn the Sensitivity down to start.
Dont expect to find stuff halfway to China, as most good things are within the first FOOT, usually less.
That's the good news.
Here's the bad news: SENSITIVITY (gain) increases cannot "suck in" what isn't there to start with. Rather, gain that is set too high only results in false signals and lots of frustration.
5. Set time limits.
a. Plan to detect for a certain amount of time, as often as possible. Like any activity, good practice makes you better.
b. DO NOT detect longer that you should - set a limit on that, too. Remember you have a job and a family and friends.
6. Set Recovery Goals.
Make it a certain coin, or artifact, a maybe a specific quota of coins, etc. Then work to achieve these goals. My goal for the summer season is to find a nice mans ring - yours can be whatever you want it to be.
Some say that this is "just a hobby, and goals are for work." DO NOT believe that crap, either. It's a load of bunk. Achievement and success at ANYTHING is utterly dependent on your ability to push yourself beyond the mundane, to go beyond the easy frontiers.
7. Carry your detector with you as much as possible.
You never know when a chance to detect will come along. But dont leave it in your car, long-term - EVER!! We're talking about sensitive, costly electronic instruments here.The heat and jostling is murder on them... and break-in thieves know what they are worth, too.
8. Learn about your area and what you might actually find.
Do a little research about every possible place you might consider detecting, from the local park to vacant lots. Like I hinted at in Tip #4, it does no good to take your detector to a barren desert where only gila monsters have ever been. I tried it once...I'm right on this, trust me. You have to go where something worth finding exists.
The park in my city was once an old home place, then a housing area through the 50's and now a modern park. The old goodies and other stuff are NOT where the hard hunted modern play grounds are - and few know it but me. Get the point?
9. Talk to your friends and family about your new hobby.
Include the strangers you meet too, like folks in the checkout line or bank tellers. Ask if they know any old places, or good modern places, where lots of people have been active. Make up some simple personal introduction cards on your computer, naming you as "Joe Schmoe, Detectorist." People respect credentials and being an ambassador of the hobby will open doors for you.
a. DO NOT be a "treasure hunter." Want to really get people stirred up, for all the wrong reasons? Mention the word "treasure" to them in earnest and see what happens.
10. Plan to do all sorts of detecting.
You are new, and this hobby has lots to offer. Dont imagine yourself only "this sort" of detectorist or "that sort." Try it all.
11. Learn the Detectorists Code of Ethics.
And practice good recovery techniques, ALL THE TIME. Few things will sour you on this hobby like being ticketed for leaving holes behind you or getting busted on private property. I learned this last one the hard way, at the wrong end of a shotgun - don't repeat my mistake
12. Get a durable carry bag at the thrift store and keep these things in it (my bag cost $3):
+ Extra headphones - A broken set of phones will ruin any hunt. Simple folding digi-phones make a nice back-up.
+ Extra batteries for your unit(s)- Likewise, a set of dead batteries is a real fun buster.
+ 2 Digging Trowels - NOT the crap from WalMart or Target's garden section. Get purpose built tools.
+ An inexpensive sand scoop. There are a surprising number of easy-digging sandy spots to hunt. You'll thank me one day for suggesting this one.
+ 2 recovery aprons - Most home centers sell nail aprons for a $1. They'll do nicely.
+ 1 10" probe - I make mine from a 3/16" piece of brazing rod and a section of old broom handle. Use this to probe for coins beneath turf areas.
+ 1 10" long screwdriver - For "popping" the coins you probe from the turf. I heated mine and hammered it into a 'spoon' shape.
+ 1 8-10" inch rugged knife - Just plain useful. Cuts roots, plugs in grass, etc. Carry it on your belt when hunting, but try to avoid worrying the "straight" people with it.
+ Garden gloves - ones you can manage dextrous work in.
+ Super glue and duct tape - you don't need this explained, right?
...You can have more but you'll need these things, sooner or later.
BONUS TIP #13: Be Patient and Determine to Have Fun!"[/size]
[size=x-small]copyright, DDH/Dahut, 2006[/size]
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Hunt smart, do research when you can, learn your detector, read the owners manual and always fill your holes.
Before you know it you will be finding all kinds of neat stuff.