Lots of great suggestions already!
I'd add that if you're naturally nervous or shy around strangers, one way to very naturally place yourself in a natural setting with something that makes sense at that moment to a perfect stranger: Buy something. Pay for something at a checkout line.
I know, intentionally vague. Here goes... I use (man, I feel like I'm giving up my best pickup line or something
) Richard Sanders Extreme Burn 2.0 in checkout lines. It's great for making a mini riot if lots of folks are around, or a very intimate organic moment that will automagically endear you to her, or blow his mind, making for them a very memorable moment that took all of 2 minutes, very few words (in fact, less is best until the bill change, body lang and eye contact!)
It's a bill changing routine, $1s to $20s like CGI effects. An amazing little bit you should always keep on you. If you don't have it, strongly recommend it, never leave home without it. Seriously.
The bit is this: walking up to pay your check, you feign leaving your wallet somewhere, pat yourself down (do a natural routine here, no Oscar's for this one)(the clerk is already thinking "oh, grrreeat"), find a small wad of $1s in your pocket count it all out and it's $5 total all the while making eye contact and acting progressively more worried and embarrassed as you make worried eye contact with the clerk while shelve watches you worriedlycount it again; 1, 2, 3, 4, 5. Yep, only $5
You've now established with out a word you don't have the cash for that $25 meal, the cashier now knows this too, you're holding the $5 you counted out. The pause is unbearable, and you wait as long as you can and exclaim "wait a minute!!..." as you now speak hesitantly but hopeful "I've got an idea, watch" using your 2 fingers to do the look here move toward the $5, count 3, and on 3 you're holding and flourishing 5 $20, the relief is palatable in your face, the relief and utter disbelief of this miracle happening out of the blue to the spectator, they never K of WHAT to do but their relief makes it always a funny time, you casually pull out 2 $20 and put them down to pay the bill, "keep the change" if that's in your financial ability, fold away the rest of the money, take your items and walk away, ask a name, leave a phone number, or if there was anyone else in line you just blew 4 complete strangers minds....giving you rapidly the confidence to try other things, approach strangers, and generally be excited to just pick some lucky bastard out of thin air and blow their minds, creating a memory they'll brag about.
Wordy I know but man that routine kills if ya pull it off naturally, the trick is an easy one so you van concentrate on the moment you're creating I met the chick at my fav Thai restaurant, met a few gals that way at the cafeteria, one lost her MIND exclaiming "did anyone else see that?!?!?" and a few in that line behind me are still trying to figure out what exactly they did see.
All strangers, every single one of them, but you've created a buildup, a moment, a mind-blowing experience complete with drama, release, laughter and a special moment all in the natural act of paying for your lunch, or buying groceries. They will not soon forget your masterful performance, only thinking it was one of those random acts of cosmic mystery that one only hears about happening to others.
Believe me, this will do wonders for your public stranger confidence and it's a helluva lotta fun doing it.
The beautiful approach on this one is there is no expectation from the unwitting spectator, just another bad day at the checkout line when some doofus forgets his wallet and only has $5.... until he instantly changes it into $20s like nothing's happened, paid the bill out of those magically created $20s and walked away into the sunset without another word.
Do this at a bar once you've done it at the corner bodega, Mcds, the grocery store, etc. People will see you. Strangers. All of them, and you now have a captive audience of one or more with which to break out into "hi, my name's Cary. If you thought that was something, here, check this out. What? Sure, where are you all sitting?". You get the picture. It's a great way to start because you are controlling every single thing to an unwitting captive audience....of strangers.
Best of luck to you with your public debut, knock em dead and don't forget us little guys!
(Thanks go to that brilliant Canadian Richard Sanders for making Extreme Burn 2.0 and all his other great routines, one of the nicest guys in the illusion fx biz)