Are there any recommended state or provinces that a non-resident can hunt moose without a guide? I am looking for an reasonable opportunity to at least see a moose, and with luck & doing my part, a chance for a shot. I am not looking for any guarantee.
I went to Newfoundland in Sept. for moose, and that is likely to be my last (in a line of) poor hunts with worse than mediocre guiding! It was bad for a long list of reasons.

You can hunt in Maine, New Hampshire, Idaho, Colorado, Utah, and Montana without a guide.
Trick is drawing the tag. It is very hard to
do. If you really want a moose go to the
forum here called Hunting reports the rest of the world. There was an excellent account of a
very high percentage moose hunt in New Foundland.

I don't think there are any states that require a guide for moose hunting. Since it appears you are in NY, you should apply for NH, VT, and ME in thier lottery since they'er close to home. Odds are long, but someone has to draw. I think ID probably has the best odds for a NR but even at that its a pretty long shot around 1-10 for the lesser areas. MT and WY are tough to draw as a NR and CO and UT are next to impossible. I applied in MT for 10 years as a resident and have been applying for the last 5 as a NR and I'm still waiting for a tag. I think I'll be lucky to draw one in the next 15... My hunting buddy applied as a resident for 17 years before he pulled a bull tag.

Applications for the moose tags in the west run from about $750 to $2500 each year! You'll get pretty much all of it back if you don't draw usually about $10-25 bucks light, but if you put in for more than one or two states to up your odds you're going to have to shell out some coins... My 'tag' fund this year was about $6k. Didn't draw squat and got it all back... but you see what I'm getting at.

I think your best bet but not the cheapest would be to go to Alaska. You can get OTC tags in quite a few units and harvest percentages are decent in some of the more remote areas. You'll have to do your homework but you should be able to get up there and back, fly into the bush, get your tags and meat and rack home for around $5000-$5500. I've put pencil to paper more times than I can count and tried it every conceivable way and pretty much the cheapest moose hunt I can come up with as a NR up there is about $4500, but it won't necessaryily be the best either. I do have a good buddy that lives up there so that would save on some of the logistics.

IMO this would probably be the biggest adventure a NR can do on his own in the lower 48... If you decide to look into that route there are a couple good books out there on DIY hunting in Alaska.

Good luck in your quest!

Well there is always Alaska.
My brother and I did a drop camp in 2005 for 10 days that turned into 13 because of rain/rain/rain. We saw a few Moose but no legal bulls and the price was $3,000 each for the fly-in and boat with gas. Total it was about $5,000 each after all the air fare, licenses, hotel, freight etc.
As for drawing a Moose tag in the lower 48 I'm beginning to think it is impossible, I've been trying to draw a Moose in Colorado as a resident since 1987 and no luck yet.
Good Luck!